Bulletin of the. Iranian Mathematical Society
|
|
- Roxanne Carson
- 6 years ago
- Views:
Transcription
1 ISSN: 7-6X Print) ISSN: Online) Bulletin of the Iranian Mathematical Society Vol 4 6), No, pp 95 Title: A note on lacunary series in Q K spaces Authors): J Zhou Published by Iranian Mathematical Society
2 Bull Iranian Math Soc Vol 4 6), No, pp 95 Online ISSN: A NOTE ON LACUNARY SERIES IN Q K SPACES J ZHOU Communicated by Ali Abkar) Abstract In this paper, under the condition that K is concave, we characterize lacunary series in Q K spaces We improve a result due to H Wulan and K Zhu Keywords: Q K spaces; lacunary series; concave MSC): Primary: 3H5; Secondary: 3B, 3H5 Introduction Let D be the unit disk in the complex plane C and denote by D the boundary of D As usual, HD) is the class of functions analytic in D The Green function in the unit disk with singularity at a D is given by gz, a) = log σ a z), z D Here σ a z) = a z az, is the Möbius transformation of D Throughout this paper, we assume that K : [, ) [, ) is an increasing function A function f HD) belongs to the space Q K if f Q K = sup f z) K gz, a)) daz) <, a D D where da is the element of Euclidean area on D normalized so that daz) = π dxdy Q K spaces are Möbius invariant in the sense that f σ a QK = f QK for every f Q K and a D See [3 5] for more results of Q K spaces If Kt) = t p, p <, then the space Q K reduces to the space Q p cf [7,8]) In particular, Q is the Dirichlet space; Q = BMOA, the space of bounded mean oscillation; Q p is the Bloch space for all p > Article electronically published on February, 6 Received: 7 September 4, Accepted: 9 November 4 95 c 6 Iranian Mathematical Society
3 if A note on lacunary series in Q K spaces 96 Recall that a function fz) = a kz HD) is called a lacunary series λ = inf k + > Such series are often used to give examples of functions in various analytic function spaces It is well known that a lacunary series belongs to BMOA if and only if it is in the Hardy space H see []) By [], if < p <, then the lacunary series f Q p if and only if n p k a k < H Wulan and K Zhu [6] characterized lacunary series in Q K spaces as follows Theorem A [6]) Let K satisfy φ K s) s ds <, ) where φ K s) = sup Kst)/Kt), < s < t Then a lacunary series fz) = a k z belongs to Q K if and only if ) a k K < By [3], the space Q K only depends on the weight function K in a neighbourhood of the origin If K t) = t log e t, < t <, then Q K is the analytic version of Q D) space see [7] and [9]) An elementary calculation shows that φ K s) = s when s Thus, K does not satisfy the condition ) In other words, Theorem A misses the case of the analytic version of Q D) space It was pointed out in [6] that Theorem A also misses the classical case of BMOA The goal of this article is to characterize lacunary series in Q K spaces under a weaker condition of K Our result covers the cases of BMOA and the analytic version of Q D) space We write A B if there exists a constant C such that A CB, in addition, the symbol A B means that A B A Main result In [6], we can find many nice estimates of the weight function K under the condition ) In recent years, the study of Q K spaces benefits from these estimates In particular, if K satisfies ), then there exists an increasing function K on, ) such that K t) Kt) for all t, ) Moreover,
4 97 Zhou K is twice differentiable on, ) and concave Namely, K t) for t, ) Next we state the main result of this paper Theorem Let K be a concave function Then a lacunary series belongs to Q K if and only if fz) = a k z ) a k K < ) Proof We prove the result by following the proof of Theorem A in [6] First suppose that fz) = a kz Q K Then D f z) K log z Bearing in mind that K is increasing, we get > ) daz) < n k a k r nk K log ) dr r n k a k e nkt Kt)dt ) a k K On the other hand, suppose that the condition ) holds Since K is concave, the estimates in [6, page 6] show that sup f z) Kgz, a))daz) r a k r k ) n K log ) dr r Write I n = {k : k < +, k N} The Hölder inequality gives a k r k) n a k r I n / r n n/ r n a k I n log ) / n/ r n a k r I n
5 A note on lacunary series in Q K spaces 98 Thus, sup f z) Kgz, a))daz) n/ a k I n Since K is increasing, we see that K e r ) / n = n K r n log ) / K log ) dr r r log ) / K log ) dr r r e nt t dt ) e s s ds If K), by [3], we can assume that K is constant Of course, Kt)/t is decreasing on, ) If K) =, we claim that Kt)/t is decreasing on, ) Choose s, t, ) such that s < t By the basic property of a concave function, we have Thus Ks) s Ks) s Kt) t = Ks) K) s = tks) skt) st Kt) Ks) t s = [sks) Kt)) + t s)ks)] st = t s [ ] Ks) Kt) Ks) t s t s Hence, Therefore, e K r n log ) / K log ) dr r r ) = n K sup f z) Kgz, a))daz) / e n t t dt ) e s s ds ) n K n k a k I n
6 99 Zhou If I n, then Using the monotonicity of Kt)/t, one gets ) ) K K This gives sup f z) Kgz, a))daz) n ) a k K I n ) a k K I n Since f is a lacunary series, then there exists a positive constant λ such that + λ > for all k It is well known that the Taylor series of fz) has at most [log λ ] + terms a k z such that I n for all n N By Hölder inequality, we obtain The proof is complete sup f z) Kgz, a))daz) [log λ ] + ) a k K I n ) a k K < ) Note that Kt) = t p, p is concave The following result follows easily from Theorem Corollary [7]) Let p [, ] Then a lacunary series fz) = a k z belongs to Q p if and only if n p k a k < Since K t) = t log e t is also concave, we have the following statement Corollary 3 [9]) A lacunary series fz) = a k z
7 A note on lacunary series in Q K spaces belongs to Q D) if and only if log + ) a k < Acknowledgment The author thanks Dr G Bao for providing a number of helpful suggestions and corrections The work is supported by NFS of Anhui Province of China No 6885MA) References [] R Aulaskari, J Xiao and R Zhao, On subspaces and subsets of BMOA and UBC, Analysis 5 995), no, [] A Baernstein, Analytic functions of bounded mean oscillation Aspects of contemporary complex analysis Proc NATO Adv Study Inst, Univ Durham, Durham, 979), 3 36, Academic Press, London-New York, 98 [3] M Essén and H Wulan, On analytic and meromorphic functions and spaces of Q K - type, Illinois J Math 46 ), no 4, [4] M Essén, H Wulan and J Xiao, Several function-theoretic characterizations of Möbius invariant Q K spaces, J Funct Anal 3 6), no, 78 5 [5] J Pau, Bounded Möbius invariant Q K spaces, J Math Anal Appl 338 8), no, 9 4 [6] H Wulan and K Zhu, Lacunary series in Q K spaces, Stud Math 78 7), no 3, 7 3 [7] J Xiao, Holomorphic Q Classes, Lecture Notes in Mathematics, 767, Springer- Verlag, Berlin, [8] J Xiao, Geometric Q p functions, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 6 [9] J Zhou and G Bao, Analytic version of Q D) space, J Math Annal Appl 4 5), no, 9 Jizhen Zhou) School of Sciences, Anhui University of Science and Technology, Huainan, Anhui 3, China address: hope89@63com
Guanlong Bao, Zengjian Lou, Ruishen Qian, and Hasi Wulan
Bull. Korean Math. Soc. 53 (2016, No. 2, pp. 561 568 http://dx.doi.org/10.4134/bkms.2016.53.2.561 ON ABSOLUTE VALUES OF Q K FUNCTIONS Guanlong Bao, Zengjian Lou, Ruishen Qian, and Hasi Wulan Abstract.
More informationWeighted Dirichlet spaces and Q p
Weighted Dirichlet spaces and Q p Nihat Gökhan Göğüş (partly joint with G. Bao and S. Pouliasis) Sabanci University CAFT 2018, Heraklion Dirichlet type spaces SETUP D = {z : z < 1} open unit disk in C.
More informationDERIVATIVE-FREE CHARACTERIZATIONS OF Q K SPACES
ERIVATIVE-FREE CHARACTERIZATIONS OF Q K SPACES HASI WULAN AN KEHE ZHU ABSTRACT. We give two characterizations of the Möbius invariant Q K spaces, one in terms of a double integral and the other in terms
More informationLacunary series in some weighted meromorphic function spaces
Mathematica Aeterna Vol. 3, 213, no. 9, 787-798 Lacunary series in some weighted meromorphic function spaces A. El-Sayed Ahmed Department of Mathematics, Faculty of Science, Taif University Box 888 El-Hawiyah,
More informationPOINTWISE MULTIPLIERS FROM WEIGHTED BERGMAN SPACES AND HARDY SPACES TO WEIGHTED BERGMAN SPACES
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 29, 24, 139 15 POINTWISE MULTIPLIERS FROM WEIGHTE BERGMAN SPACES AN HARY SPACES TO WEIGHTE BERGMAN SPACES Ruhan Zhao University of Toledo, epartment
More informationVOLUME INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS
VOLUME INTEGRAL MEANS OF HOLOMORPHIC FUNCTIONS JIE XIAO AND KEHE ZHU ABSTRACT. The classical integral means of a holomorphic function f in the unit disk are defined by [ 1/p 1 2π f(re iθ ) dθ] p, r < 1.
More informationRiemann-Stieltjes Operators between Weighted Bloch and Weighted Bergman Spaces
Int. J. Contemp. Math. Sci., Vol. 2, 2007, no. 16, 759-772 Riemann-Stieltjes Operators between Weighted Bloch and Weighted Bergman Spaces Ajay K. Sharma 1 School of Applied Physics and Mathematics Shri
More informationD K spaces and Carleson measures
D K spaces and Carleson measures Joint with Hasi Wulan and Ruhan Zhao The College at Brockport, State University of New York, Mathematics Department March 17, 2017 Notations Let D denote the unit disc
More informationA HARDY LITTLEWOOD THEOREM FOR BERGMAN SPACES
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 43, 2018, 807 821 A HARY LITTLEWOO THEOREM FOR BERGMAN SPACES Guanlong Bao, Hasi Wulan and Kehe Zhu Shantou University, epartment of Mathematics
More informationA Version of the Lohwater-Pommerenke Theorem for Strongly Normal Functions
Computational Methods and Function Theory Volume 1 2001), No. 1, 99 105 A Version of the Lohwater-Pommerenke Theorem for Strongly Normal Functions Rauno Aulaskari and Hasi Wulan Abstract. A new characterization
More informationBulletin of the. Iranian Mathematical Society
ISSN: 07-060X (Print) ISSN: 735-855 (Online) Bulletin of the Iranian Mathematical Society Vol 4 (05), No 6, pp 5 57 Title: The Libera operator on Dirichlet spaces Author(s): G Bao and J Yang Published
More informationarxiv: v1 [math.cv] 21 Sep 2007
Proc. Indian Acad. Sci. (Math. Sci. Vol. 117, No. 3, August 2003, pp. 371 385. Printed in India Weighted composition operators from Bergman-type spaces into Bloch spaces arxiv:0709.3347v1 [math.cv] 21
More informationResearch Article Distance from Bloch-Type Functions to the Analytic Space
Abstract and Applied Analysis, Article I 60237, 7 pages http://dx.doi.org/0.55/204/60237 Research Article istance from Bloch-Type Functions to the Analytic Space F(p, q, s Cheng Yuan and Cezhong Tong 2
More informationStrict singularity of a Volterra-type integral operator on H p
Strict singularity of a Volterra-type integral operator on H p Santeri Miihkinen, University of Eastern Finland IWOTA Chemnitz, 14-18 August 2017 Santeri Miihkinen, UEF Volterra-type integral operator
More informationINTEGRATION OPERATORS FROM CAUCHY INTEGRAL TRANSFORMS TO WEIGHTED DIRICHLET SPACES. Ajay K. Sharma and Anshu Sharma (Received 16 April, 2013)
NEW ZEALAN JOURNAL OF MATHEMATICS Volume 44 (204), 93 0 INTEGRATION OPERATORS FROM CAUCHY INTEGRAL TRANSFORMS TO WEIGHTE IRICHLET SPACES Ajay K. Sharma and Anshu Sharma (Received 6 April, 203) Abstract.
More informationTRANSLATION INVARIANCE OF FOCK SPACES
TRANSLATION INVARIANCE OF FOCK SPACES KEHE ZHU ABSTRACT. We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.
More informationCOMPOSITION SEMIGROUPS ON BMOA AND H AUSTIN ANDERSON, MIRJANA JOVOVIC, AND WAYNE SMITH
COMPOSITION SEMIGROUPS ON BMOA AND H AUSTIN ANDERSON, MIRJANA JOVOVIC, AND WAYNE SMITH Abstract. We study [ϕ t, X], the maximal space of strong continuity for a semigroup of composition operators induced
More information引用北海学園大学学園論集 (171): 11-24
タイトル 著者 On Some Singular Integral Operato One to One Mappings on the Weight Hilbert Spaces YAMAMOTO, Takanori 引用北海学園大学学園論集 (171): 11-24 発行日 2017-03-25 On Some Singular Integral Operators Which are One
More informationWEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES
Acta Mathematica Scientia 20,3B(2):64 65 http://actams.wipm.ac.cn WEIGHTE COMPOSITION OPERATORS BETWEEN IRICHLET SPACES Wang Maofa ( ) School of Mathematics and Statistics, Wuhan University, Wuhan 430072,
More informationBLOCH FUNCTIONS ON THE UNIT BALL OF AN INFINITE DIMENSIONAL HILBERT SPACE
BLOCH FUNCTIONS ON THE UNIT BALL OF AN INFINITE DIMENSIONAL HILBERT SPACE OSCAR BLASCO, PABLO GALINDO, AND ALEJANDRO MIRALLES Abstract. The Bloch space has been studied on the open unit disk of C and some
More informationIntegral operators on analytic Morrey spaces
SCIENCE CHINA Mathematics ARTICLES September 4 Vol 57 No 9: 96 974 doi: 7/s45-4-48-5 Integral operators on analytic Morrey spaces LI PengTao, LIU JunMing & LOU ZengJian epartment of Mathematics, Shantou
More informationWeighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space
DOI: 10.1515/auom-2016-0056 An. Şt. Univ. Ovidius Constanţa Vol. 24(3),2016, 223 240 Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space Songxiao
More informationTHE HYPERBOLIC METRIC OF A RECTANGLE
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 26, 2001, 401 407 THE HYPERBOLIC METRIC OF A RECTANGLE A. F. Beardon University of Cambridge, DPMMS, Centre for Mathematical Sciences Wilberforce
More informationGROWTH OF SOLUTIONS TO HIGHER ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS IN ANGULAR DOMAINS
Electronic Journal of Differential Equations, Vol 200(200), No 64, pp 7 ISSN: 072-669 URL: http://ejdemathtxstateedu or http://ejdemathuntedu ftp ejdemathtxstateedu GROWTH OF SOLUTIONS TO HIGHER ORDER
More informationRESEARCH STATEMENT. Introduction
RESEARCH STATEMENT PRITHA CHAKRABORTY Introduction My primary research interests lie in complex analysis (in one variable), especially in complex-valued analytic function spaces and their applications
More informationfunctions Möbius invariant spaces
Inner functions in Möbius invariant spaces Fernando Pérez-González (U. La Laguna) and Jouni Rättyä (U. Eastern Finland-Joensuu) CHARM 2011, Málaga Introduction An analytic function in the unit disc D :=
More informationBulletin of the. Iranian Mathematical Society
ISSN: 1017-060X (Print) ISSN: 1735-8515 (Online) Bulletin of the Iranian Mathematical Society Vol. 41 (2015), No. 3, pp. 581 590. Title: Volume difference inequalities for the projection and intersection
More informationBLOCH SPACE AND THE NORM OF THE BERGMAN PROJECTION
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 38, 2013, 849 853 BLOCH SPACE AN THE NORM OF THE BERGMAN PROJECTION Antti Perälä University of Helsinki, epartment of Mathematics and Statistics
More informationPacific Journal of Mathematics
Pacific Journal of Mathematics THE Q p CORONA THEOREM Jie Xiao Volume 194 No. 2 June 2000 PACIFIC JOURNAL OF MATHEMATICS Vol. 194, No. 2, 2000 THE Q p CORONA THEOREM Jie Xiao For p (0, 1), let Q p be
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. 6 (2012), no. 1, 139 146 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) www.emis.de/journals/bjma/ AN EXTENSION OF KY FAN S DOMINANCE THEOREM RAHIM ALIZADEH
More informationComposition Operators from Hardy-Orlicz Spaces to Bloch-Orlicz Type Spaces
Journal of Mathematical Research with Applications Sept., 018, Vol. 38, No. 5, pp. 458 464 OI:10.3770/j.issn:095-651.018.05.003 Http://jmre.dlut.edu.cn Composition Operators from Hardy-Orlicz Spaces to
More informationAccumulation constants of iterated function systems with Bloch target domains
Accumulation constants of iterated function systems with Bloch target domains September 29, 2005 1 Introduction Linda Keen and Nikola Lakic 1 Suppose that we are given a random sequence of holomorphic
More informationarxiv: v1 [math.fa] 13 Jul 2007
Proc. Indian Acad. Sci. (Math. Sci.) Vol. 117, No. 2, May 2003, pp. 185 195. Printed in India Weighted composition operators on weighted Bergman spaces of bounded symmetric domains arxiv:0707.1964v1 [math.fa]
More informationINTEGRAL MEANS AND COEFFICIENT ESTIMATES ON PLANAR HARMONIC MAPPINGS
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 37 69 79 INTEGRAL MEANS AND COEFFICIENT ESTIMATES ON PLANAR HARMONIC MAPPINGS Shaolin Chen Saminathan Ponnusamy and Xiantao Wang Hunan Normal University
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. 2 (2008), no., 70 77 Banach Journal of Mathematical Analysis ISSN: 735-8787 (electronic) http://www.math-analysis.org WIDTH-INTEGRALS AND AFFINE SURFACE AREA OF CONVEX BODIES WING-SUM
More informationPRODUCTS OF TOEPLITZ OPERATORS ON THE FOCK SPACE
PRODUCTS OF TOEPLITZ OPERATORS ON THE FOCK SPACE HONG RAE CHO, JONG-DO PARK, AND KEHE ZHU ABSTRACT. Let f and g be functions, not identically zero, in the Fock space F 2 α of. We show that the product
More informationCOMPOSITION OPERATORS ON ANALYTIC WEIGHTED HILBERT SPACES
COMPOSITION OPERATORS ON ANALYTIC WEIGHTE HILBERT SPACES K. KELLAY Abstract. We consider composition operators in the analytic weighted Hilbert space. Various criteria on boundedness, compactness and Hilbert-Schmidt
More informationFunction Spaces - selected open problems
Contemporary Mathematics Function Spaces - selected open problems Krzysztof Jarosz Abstract. We discuss briefly selected open problems concerning various function spaces. 1. Introduction We discuss several
More informationWeighted composition operators on weighted Bergman spaces of bounded symmetric domains
Proc. Indian Acad. Sci. (Math. Sci.) Vol. 117, No. 2, May 2007, pp. 185 196. Printed in India Weighted composition operators on weighted Bergman spaces of bounded symmetric domains SANJAY KUMAR and KANWAR
More informationSAMPLING SEQUENCES FOR BERGMAN SPACES FOR p < 1. Alexander P. Schuster and Dror Varolin
SAMPLING SEQUENCES FOR BERGMAN SPACES FOR p < Alexander P. Schuster and ror Varolin Abstract. We provide a proof of the sufficiency direction of Seip s characterization of sampling sequences for Bergman
More informationPRODUCTS OF MULTIPLICATION, COMPOSITION AND DIFFERENTIATION OPERATORS FROM MIXED-NORM SPACES TO WEIGHTED-TYPE SPACES. Fang Zhang and Yongmin Liu
TAIWANESE JOURNAL OF MATHEMATICS Vol. 18, No. 6, pp. 1927-1940, December 2014 DOI: 10.11650/tjm.18.2014.4311 This paper is available online at http://journal.taiwanmathsoc.org.tw PRODUCTS OF MULTIPLICATION,
More informationDIMENSIONS OF JULIA SETS OF HYPERBOLIC ENTIRE FUNCTIONS
Bull. London Math. Soc. 36 2004 263 270 C 2004 London Mathematical Society DOI: 10.1112/S0024609303002698 DIMENSIONS OF JULIA SETS OF HYPERBOLIC ENTIRE FUNCTIONS GWYNETH M. STALLARD Abstract It is known
More informationSOME CLOSED RANGE INTEGRAL OPERATORS ON SPACES OF ANALYTIC FUNCTIONS
SOME CLOSE RANGE INTEGRAL OPERATORS ON SPACES OF ANALYTIC FUNCTIONS Austin Anderson epartment of Mathematics University of Hawaii Honolulu, Hawaii 96822 austina@hawaii.edu Abstract: Our main result is
More informationON GENERALIZED SCHWARZ-PICK ESTIMATES
ON GENERALIZED SCHWARZ-PICK ESTIMATES J. M. ANDERSON AND J. ROVNYAK. Introduction By Pick s invariant form of Schwarz s lemma, an analytic function B(z) which is bounded by one in the unit disk D = {z
More informationTHE THERMODYNAMIC FORMALISM APPROACH TO SELBERG'S ZETA FUNCTION FOR PSL(2, Z)
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 25, Number 1, July 1991 THE THERMODYNAMIC FORMALISM APPROACH TO SELBERG'S ZETA FUNCTION FOR PSL(2, Z) DIETER H. MAYER I. INTRODUCTION Besides
More informationPolarization constant K(n, X) = 1 for entire functions of exponential type
Int. J. Nonlinear Anal. Appl. 6 (2015) No. 2, 35-45 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.252 Polarization constant K(n, X) = 1 for entire functions of exponential type A.
More informationBulletin of the Iranian Mathematical Society
ISSN: 7-6X (Print ISSN: 735-855 (Online Special Issue of the ulletin of the Iranian Mathematical Society in Honor of Professor Heydar Radjavi s 8th irthday Vol. 4 (5, No. 7, pp. 85 94. Title: Submajorization
More informationINEQUALITIES FOR SUMS OF INDEPENDENT RANDOM VARIABLES IN LORENTZ SPACES
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 45, Number 5, 2015 INEQUALITIES FOR SUMS OF INDEPENDENT RANDOM VARIABLES IN LORENTZ SPACES GHADIR SADEGHI ABSTRACT. By using interpolation with a function parameter,
More informationCONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES. Jong Soo Jung. 1. Introduction
Korean J. Math. 16 (2008), No. 2, pp. 215 231 CONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES Jong Soo Jung Abstract. Let E be a uniformly convex Banach space
More informationStrong continuity of semigroups of composition operators on Morre
Semigroups on Strong continuity of semigroups of composition operators on Noel Merchán Universidad de Málaga, Spain Joint work with Petros Galanopoulos and Aristomenis G. Siskakis New Developments in Complex
More informationSOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH EXCEPTIONALLY FEW ZEROS
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 23, 1998, 429 452 SOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH EXCEPTIONALLY FEW ZEROS Gary G. Gundersen, Enid M. Steinbart, and
More informationA NOTE ON A BASIS PROBLEM
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 51, Number 2, September 1975 A NOTE ON A BASIS PROBLEM J. M. ANDERSON ABSTRACT. It is shown that the functions {exp xvx\v_. form a basis for the
More informationON HARMONIC FUNCTIONS ON SURFACES WITH POSITIVE GAUSS CURVATURE AND THE SCHWARZ LEMMA
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 44, Number 5, 24 ON HARMONIC FUNCTIONS ON SURFACES WITH POSITIVE GAUSS CURVATURE AND THE SCHWARZ LEMMA DAVID KALAJ ABSTRACT. We prove some versions of the Schwarz
More informationCOMPOSITION OPERATORS ON HARDY-SOBOLEV SPACES
Indian J. Pure Appl. Math., 46(3): 55-67, June 015 c Indian National Science Academy DOI: 10.1007/s136-015-0115-x COMPOSITION OPERATORS ON HARDY-SOBOLEV SPACES Li He, Guang Fu Cao 1 and Zhong Hua He Department
More informationMIXED NORMS AND ANALYTIC FUNCTION SPACES. By Stephen M. Buckley Department of Mathematics, National University of Ireland, Maynooth
MIXED NORMS AND ANALYTIC FUNCTION SPACES By Stephen M. Buckley Department of Mathematics, National University of Ireland, Maynooth Abstract We define and investigate general mixed-norm type sequence spaces,
More informationFixed points of the derivative and k-th power of solutions of complex linear differential equations in the unit disc
Electronic Journal of Qualitative Theory of Differential Equations 2009, No. 48, -9; http://www.math.u-szeged.hu/ejqtde/ Fixed points of the derivative and -th power of solutions of complex linear differential
More informationComposition operators between weighted Bergman spaces and weighted Banach spaces of holomorphic functions
Irish Math. Soc. Bulletin Number 79, Summer 07, 75 85 ISSN 079-5578 Composition operators between weighted Bergman spaces and weighted Banach spaces of holomorphic functions ELKE WOLF Abstract. An analytic
More informationEXTREMAL DOMAINS FOR SELF-COMMUTATORS IN THE BERGMAN SPACE
EXTREMAL DOMAINS FOR SELF-COMMUTATORS IN THE BERGMAN SPACE MATTHEW FLEEMAN AND DMITRY KHAVINSON Abstract. In [10], the authors have shown that Putnam's inequality for the norm of self-commutators can be
More informationRANDOM HOLOMORPHIC ITERATIONS AND DEGENERATE SUBDOMAINS OF THE UNIT DISK
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000 000 S 0002-9939(XX)0000-0 RANDOM HOLOMORPHIC ITERATIONS AND DEGENERATE SUBDOMAINS OF THE UNIT DISK LINDA KEEN AND NIKOLA
More informationA NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 32010), Pages 109-121. A NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS S.
More informationInternational Journal of Pure and Applied Mathematics Volume 60 No ,
International Journal of Pure and Applied Mathematics Volume 60 No. 3 200, 259-267 ON CERTAIN CLASS OF SZÁSZ-MIRAKYAN OPERATORS IN EXPONENTIAL WEIGHT SPACES Lucyna Rempulska, Szymon Graczyk 2,2 Institute
More informationUNCERTAINTY PRINCIPLES FOR THE FOCK SPACE
UNCERTAINTY PRINCIPLES FOR THE FOCK SPACE KEHE ZHU ABSTRACT. We prove several versions of the uncertainty principle for the Fock space F 2 in the complex plane. In particular, for any unit vector f in
More informationResearch Article Product of Extended Cesàro Operator and Composition Operator from Lipschitz Space to F p, q, s Space on the Unit Ball
Abstract and Applied Analysis Volume 2011, Article ID 152635, 9 pages doi:10.1155/2011/152635 Research Article Product of Extended Cesàro Operator and Composition Operator from Lipschitz Space to F p,
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics SOME NORMALITY CRITERIA INDRAJIT LAHIRI AND SHYAMALI DEWAN Department of Mathematics University of Kalyani West Bengal 741235, India. EMail: indrajit@cal2.vsnl.net.in
More informationTHE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS. Communicated by Mohammad Sal Moslehian. 1.
Bulletin of the Iranian Mathematical Society Vol. 35 No. (009 ), pp 119-14. THE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS R.M. ALI, S.K. LEE, V. RAVICHANDRAN AND S. SUPRAMANIAM
More informationDeficiency And Relative Deficiency Of E-Valued Meromorphic Functions
Applied Mathematics E-Notes, 323, -8 c ISSN 67-25 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Deficiency And Relative Deficiency Of E-Valued Meromorphic Functions Zhaojun Wu, Zuxing
More informationON BOUNDEDNESS OF MAXIMAL FUNCTIONS IN SOBOLEV SPACES
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 29, 2004, 167 176 ON BOUNDEDNESS OF MAXIMAL FUNCTIONS IN SOBOLEV SPACES Piotr Haj lasz and Jani Onninen Warsaw University, Institute of Mathematics
More informationADJOINT OPERATOR OF BERGMAN PROJECTION AND BESOV SPACE B 1
AJOINT OPERATOR OF BERGMAN PROJECTION AN BESOV SPACE B 1 AVI KALAJ and JORJIJE VUJAINOVIĆ The main result of this paper is related to finding two-sided bounds of norm for the adjoint operator P of the
More informationEXISTENCE OF NON-SUBNORMAL POLYNOMIALLY HYPONORMAL OPERATORS
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 25, Number 2, October 1991 EXISTENCE OF NON-SUBNORMAL POLYNOMIALLY HYPONORMAL OPERATORS RAUL E. CURTO AND MIHAI PUTINAR INTRODUCTION In
More informationBulletin of the Iranian Mathematical Society
ISSN: 1017-060X (Print) ISSN: 1735-8515 (Online) Special Issue of the Bulletin of the Iranian Mathematical Society in Honor of Professor Freydoon Shahidi s 70th birthday Vol. 43 (2017), No. 4, pp. 313
More informationL p -Width-Integrals and Affine Surface Areas
LIBERTAS MATHEMATICA, vol XXX (2010) L p -Width-Integrals and Affine Surface Areas Chang-jian ZHAO and Mihály BENCZE Abstract. The main purposes of this paper are to establish some new Brunn- Minkowski
More informationComposition operators: the essential norm and norm-attaining
Composition operators: the essential norm and norm-attaining Mikael Lindström Department of Mathematical Sciences University of Oulu Valencia, April, 2011 The purpose of this talk is to first discuss the
More informationActa Univ. Sapientiae, Mathematica, 6, 1 (2014) RETRACTED
Acta Univ. Sapientiae, Mathematica, 6, (204) 07 6 Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions Elke Wolf University of Paderborn
More informationConvergence theorems for a finite family. of nonspreading and nonexpansive. multivalued mappings and equilibrium. problems with application
Theoretical Mathematics & Applications, vol.3, no.3, 2013, 49-61 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2013 Convergence theorems for a finite family of nonspreading and nonexpansive
More informationWEIGHTED COMPOSITION OPERATORS BETWEEN H AND THE BLOCH SPACE. Sh^uichi Ohno 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol. 5, No. 3, pp. 555-563, September 2001 This paper is available online at http://www.math.nthu.edu.tw/tjm/ WEIGHTED COMPOSITION OPERATORS BETWEEN H AND THE BLOCH SPACE
More informationHong Rae Cho and Ern Gun Kwon. dv q
J Korean Math Soc 4 (23), No 3, pp 435 445 SOBOLEV-TYPE EMBEING THEOREMS FOR HARMONIC AN HOLOMORPHIC SOBOLEV SPACES Hong Rae Cho and Ern Gun Kwon Abstract In this paper we consider Sobolev-type embedding
More informationA Class of Univalent Harmonic Mappings
Mathematica Aeterna, Vol. 6, 016, no. 5, 675-680 A Class of Univalent Harmonic Mappings Jinjing Qiao Department of Mathematics, Hebei University, Baoding, Hebei 07100, People s Republic of China Qiannan
More informationNonarchimedean Cantor set and string
J fixed point theory appl Online First c 2008 Birkhäuser Verlag Basel/Switzerland DOI 101007/s11784-008-0062-9 Journal of Fixed Point Theory and Applications Nonarchimedean Cantor set and string Michel
More informationMEROMORPHIC FUNCTIONS AND ALSO THEIR FIRST TWO DERIVATIVES HAVE THE SAME ZEROS
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 30, 2005, 205 28 MEROMORPHIC FUNCTIONS AND ALSO THEIR FIRST TWO DERIVATIVES HAVE THE SAME ZEROS Lian-Zhong Yang Shandong University, School of Mathematics
More informationON OPERATORS WITH AN ABSOLUTE VALUE CONDITION. In Ho Jeon and B. P. Duggal. 1. Introduction
J. Korean Math. Soc. 41 (2004), No. 4, pp. 617 627 ON OPERATORS WITH AN ABSOLUTE VALUE CONDITION In Ho Jeon and B. P. Duggal Abstract. Let A denote the class of bounded linear Hilbert space operators with
More informationRESEARCH ANNOUNCEMENTS PROJECTIONS OF C AUTOMORPHIC FORMS BY JACOB STURM 1
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 2, Number 3, May 1980 RESEARCH ANNOUNCEMENTS PROJECTIONS OF C AUTOMORPHIC FORMS BY JACOB STURM 1 The purpose of this paper is to exhibit
More informationWeakly Compact Composition Operators on Hardy Spaces of the Upper Half-Plane 1
Int. Journal of Math. Analysis, Vol. 4, 2010, no. 37, 1851-1856 Weakly Compact Composition Operators on Hardy Spaces of the Upper Half-Plane 1 Hong Bin Bai School of Science Sichuan University of Science
More informationM. MATELJEVIC AND M. PAVLOVIC. to X, where X is BMOA, VMOA, 3S or ^ 0
PACIFIC JOURNAL OF MATHEMATICS Vol. 146, No. 1, 1990 MULTIPLIERS OF H p AND BMOA M. MATELJEVIC AND M. PAVLOVIC We characterize the multipliers from H ι to X, where X is BMOA, VMOA, 3S or ^ 0 and from H
More informationON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 3, 2018 ISSN 1223-7027 ON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES Vahid Dadashi 1 In this paper, we introduce a hybrid projection algorithm for a countable
More informationHYPERBOLIC DERIVATIVES AND GENERALIZED SCHWARZ-PICK ESTIMATES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 132, Number 11, Pages 339 3318 S 2-9939(4)7479-9 Article electronically published on May 12, 24 HYPERBOLIC DERIVATIVES AND GENERALIZED SCHWARZ-PICK
More informationCoecient bounds for certain subclasses of analytic functions of complex order
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1015 1022 Coecient bounds for certain subclasses of analytic functions of complex order Serap Bulut Abstract In this paper, we introduce
More informationOn the simplest expression of the perturbed Moore Penrose metric generalized inverse
Annals of the University of Bucharest (mathematical series) 4 (LXII) (2013), 433 446 On the simplest expression of the perturbed Moore Penrose metric generalized inverse Jianbing Cao and Yifeng Xue Communicated
More informationOn Quasi-Hadamard Product of Certain Classes of Analytic Functions
Bulletin of Mathematical analysis Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 36-46 On Quasi-Hadamard Product of Certain Classes of Analytic Functions Wei-Ping
More informationNOTE ON HILBERT-SCHMIDT COMPOSITION OPERATORS ON WEIGHTED HARDY SPACES
NOTE ON HILBERT-SCHMIDT COMPOSITION OPERATORS ON WEIGHTED HARDY SPACES THEMIS MITSIS DEPARTMENT OF MATHEMATICS UNIVERSITY OF CRETE KNOSSOS AVE. 7149 IRAKLIO GREECE Abstract. We show that if C ϕ is a Hilbert-Schmidt
More informationQUASINORMAL FAMILIES AND PERIODIC POINTS
QUASINORMAL FAMILIES AND PERIODIC POINTS WALTER BERGWEILER Dedicated to Larry Zalcman on his 60th Birthday Abstract. Let n 2 be an integer and K > 1. By f n we denote the n-th iterate of a function f.
More informationEXTENSIONS OF THE BLOCH PÓLYA THEOREM ON THE NUMBER OF REAL ZEROS OF POLYNOMIALS
EXTENSIONS OF THE BLOCH PÓLYA THEOREM ON THE NUMBER OF REAL ZEROS OF POLYNOMIALS Tamás Erdélyi Abstract. We prove that there are absolute constants c 1 > 0 and c 2 > 0 for every {a 0, a 1,..., a n } [1,
More informationOn Kusuoka Representation of Law Invariant Risk Measures
MATHEMATICS OF OPERATIONS RESEARCH Vol. 38, No. 1, February 213, pp. 142 152 ISSN 364-765X (print) ISSN 1526-5471 (online) http://dx.doi.org/1.1287/moor.112.563 213 INFORMS On Kusuoka Representation of
More information2 Simply connected domains
RESEARCH A note on the Königs domain of compact composition operators on the Bloch space Matthew M Jones Open Access Correspondence: m.m.jones@mdx. ac.uk Department of Mathematics, Middlesex University,
More informationPERIODIC PROBLEMS WITH φ-laplacian INVOLVING NON-ORDERED LOWER AND UPPER FUNCTIONS
Fixed Point Theory, Volume 6, No. 1, 25, 99-112 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm PERIODIC PROBLEMS WITH φ-laplacian INVOLVING NON-ORDERED LOWER AND UPPER FUNCTIONS IRENA RACHŮNKOVÁ1 AND MILAN
More informationarxiv: v1 [math.oc] 21 Mar 2015
Convex KKM maps, monotone operators and Minty variational inequalities arxiv:1503.06363v1 [math.oc] 21 Mar 2015 Marc Lassonde Université des Antilles, 97159 Pointe à Pitre, France E-mail: marc.lassonde@univ-ag.fr
More informationON COMPACTNESS OF THE DIFFERENCE OF COMPOSITION OPERATORS. C φ 2 e = lim sup w 1
ON COMPACTNESS OF THE DIFFERENCE OF COMPOSITION OPERATORS PEKKA NIEMINEN AND EERO SAKSMAN Abstract. We give a negative answer to a conjecture of J. E. Shapiro concerning compactness of the dierence of
More informationBoundedness and Regularizing Effects of O Hara s Knot Energies
March, 2 2:24 WSPC/INSTRUCTION FILE OHarasEnergies Boundedness and Regularizing Effects of O Hara s Knot Energies Simon Blatt Departement Mathematik ETH Zürich Rämistrasse CH-84 Zürich Switzerland simon.blatt@math.ethz.ch
More informationBulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp
Bulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp 1125-1135. COMMON FIXED POINTS OF A FINITE FAMILY OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES A. BUNYAWAT
More informationn(t,f) n(0,f) dt+n(0,f)logr t log + f(re iθ ) dθ.
Bull. Korean Math. Soc. 53 (2016), No. 1, pp. 29 38 http://dx.doi.org/10.4134/bkms.2016.53.1.029 VALUE DISTRIBUTION OF SOME q-difference POLYNOMIALS Na Xu and Chun-Ping Zhong Abstract. For a transcendental
More informationEXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS WITH UNBOUNDED POTENTIAL. 1. Introduction In this article, we consider the Kirchhoff type problem
Electronic Journal of Differential Equations, Vol. 207 (207), No. 84, pp. 2. ISSN: 072-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS
More information