On geometric properties of the spaces L p(x)
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1 Jaroslav Lukeš, Luboš Pick, Dušan Pokorný On geometric properties of the spaces L p(x) Preprint No. MATH-KMA-2008/290 December 2008 Submitted Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8, Czech Republic
2 Cover print by Reprostředisko, Malostranské nám. 25, Praha 1 - Malá Strana Design by Mirko Rokyta, picture of snowflake by Ondřej Kalenda Current series administrator: Mirko Rokyta
3 List of preprints released in this series All preprints available on contact to series administrator:
4 For the details on the 219 papers submitted in years see the web page of the preprint series [MATH-KMA 2007/220] Eva Murtinová: On (weakly) Whyburn spaces. [MATH-KMA 2007/221] Petr Holický, C.E. Weil, Luděk Zajíček: A note on the Darboux property of Fréchet derivatives. [MATH-KMA 2007/222] Josef Daněček, Oldřich John, Jana Stará: Remarks on C 1,γ regularity of weak solutions to elliptic systems with BMO gradients. [MATH-KMA 2007/223] Tomáš Bárta: Delayed quasilinear evolution equations with application to heat flow. [MATH-KMA 2007/224] Dalibor Pražák: Exponential attractors for abstract parabolic systems with bounded delay. [MATH-KMA 2007/225] Tomáš Bárta: A generation theorem for hyperbolic equations with coefficients of bounded variation in time. [MATH-KMA 2007/226] Eduard Feireisl, Dalibor Pražák: A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid. [MATH-KMA 2007/227] A. Avilés, Ondřej Kalenda: Fiber orders and compact spaces of uncountable weight. [MATH-KMA 2007/228] Andrea Cianchi, Ron Kerman, Luboš Pick: Trace inequalities and rearrangements. [MATH-KMA 2007/229] Miroslav Hušek: Urysohn universal space, its development and Hausdorff s approach. [MATH-KMA 2007/230] Ondrej Kurka: Reflexivity and sets of Fréchet subdifferentiability. [MATH-KMA 2007/231] Miroslav Pošta: On partial regularity of solutions to the quasilinear parabolic system up to the boundary. [MATH-KMA 2007/232] Stanislav Hencl, Pekka Koskela, Jani Onninen: Homeomorphisms of bounded variation. [MATH-KMA 2007/233] Ondřej Kalenda: On products with the unit interval. [MATH-KMA 2007/234] Miroslav Bačák, Jiří Spurný: Complementability of spaces of affine continuous functions on simplices. [MATH-KMA 2007/235] Jaroslav Milota: Invitation to mathematical control theory. [MATH-KMA 2007/236] David Chodounský, Eva Murtinová: Internal normality and internal compactness. [MATH-KMA 2007/237] Ondřej Kurka: On Borel classes of sets of Fréchet subdifferentiability. [MATH-KMA 2007/238] Jiří Spurný: The Dirichlet problem for Baire-two functions on simplices. [MATH-KMA 2007/239] Jiří Spurný: Automatic boundedness of affine functions. [MATH-KMA 2007/240] Jiří Spurný, Miroslav Zelený: Additive families of low Borel classes and Borel measurable selectors. [MATH-KMA 2007/241] Petr Holický, Ondřej Kalenda, Libor Veselý, Luděk Zajíček: Quotients of continuous convex functions on nonreflexive Banach spaces. [MATH-KMA 2007/242] Libor Veselý, Luděk Zajíček: On compositions of d.c. functions and mappings. [MATH-KMA 2007/243] Luděk Zajíček: A C 1 function which is nowhere strongly paraconvex and nowhere semiconcave. [MATH-KMA 2007/244] Libor Veselý, Luděk Zajíček: On vector functions of bounded convexity. [MATH-KMA 2007/245] Tomáš Bárta: Polynomial decay for solutions of hyperbolic integrodifferential equations. [MATH-KMA 2007/246] Tomáš Bárta: On R-sectorial derivatives on Bergman spaces. [MATH-KMA 2007/247] Ondřej Kalenda: Natural examples of Valdivia compact spaces. [MATH-KMA 2007/248] Antonín Procházka: Winning tactics in a geometrical game. [MATH-KMA 2007/249] Étienne Matheron, Miroslav Zelený: Descriptive set theory of families of small sets. [MATH-KMA 2007/250] Jiří Spurný: The boundary problem for L 1 preduals. [MATH-KMA 2007/251] Amiran Gogatishvili, Luboš Pick: Calderón-type theorems for operators of non-standard endpoint behavior. [MATH-KMA 2007/252] Marianna Csörnyei, Stanislav Hencl, Jan Malý: Homeomorphisms in the Sobolev space W 1,n 1.
5 [MATH-KMA 2007/253] Jiří Spurný: On the Dirichlet problem of extreme points for non-continuous functions. [MATH-KMA 2007/254] Miroslav Bačák: Point simpliciality in the Choquet theory. [MATH-KMA 2007/255] Ondřej Kurka: Structure of the set of norm-attaining functionals on strictly convex spaces [MATH-KMA 2008/256] Miroslav Bulíček, Dalibor Pražák: A note on the dimension of the global attractor for abstract semilinear hyperbolic problem. [MATH-KMA 2008/257] Eva Fašangová, Pedro J. Miana: Hilbert, Dirichlet and Fejér families of operators arising from C 0 -groups and cosine functions. [MATH-KMA 2008/258] Josef Daněček, Oldřich John, Jana Stará: On the Hölder continuity of gradient of solutions to a class of elliptic systems. [MATH-KMA 2008/259] Jakub Duda, Luděk Zajíček: Semiconvex functions: representations as suprema of smooth functions and extensions. [MATH-KMA 2008/260] Jakub Duda, Luděk Zajíček: Curves in Banach spaces which allow a C 2 parametrization. [MATH-KMA 2008/261] Václav Vlasák, Miroslav Zelený: Compact sets of continuity for Borel functions. [MATH-KMA 2008/262] Ondřej Kalenda, Jiří Spurný: Boundaries of compact convex sets and fragmentability. [MATH-KMA 2008/263] Ondřej Kurka, Dušan Pokorný: Porosity and the Darboux property of Fréchet derivatives. [MATH-KMA 2008/264] Miroslav Kačena, Jiří Spurný: Affine images of compact convex sets and maximal measures. [MATH-KMA 2008/265] Miroslav Kačena: Products and projective limits of function spaces. [MATH-KMA 2008/266] Miroslav Bačák: Minimal measures and nonsimplicial function cones. [MATH-KMA 2008/267] Miroslav Bačák, Petr Hájek: Mazur intersection property for Asplund spaces. [MATH-KMA 2008/268] Stanislav Hencl: On the weak differentiability of u f 1. [MATH-KMA 2008/269] Amiran Gogatishvili, Luboš Pick, Jan Schneider: The rearrangement-invariant hull of a Besov space. [MATH-KMA 2008/270] Ron Kerman, Luboš Pick: Explicit formulas for optimal rearrangementinvariant norms in Sobolev imbedding inequalities. [MATH-KMA 2008/271] Petr Holický: Decompositions of Borel bimeasurable mappings between complete metric spaces. [MATH-KMA 2008/272] Luboš Pick: Optimality of function spaces in Sobolev embeddings. [MATH-KMA 2008/273] Jiří Spurný: Borel sets and functions in topological spaces. [MATH-KMA 2008/274] Miroslav Kačena, Jiří Spurný: Affine Baire functions on Choquet simplices. [MATH-KMA 2008/275] Jiří Jelínek, Dalibor Pražák: On the sign of Colombeau functions and applications to conservation laws. [MATH-KMA 2008/276] Warren B. Moors, Jiří Spurný: On the topology of pointwise convergence on the boundaries of L 1 -predual. [MATH-KMA 2008/277] Hugo Beirão da Veiga, Petr Kaplický, Michael Růžička: Boundary regularity of shear thickening flows. [MATH-KMA 2008/278] Petr Hájek, Gilles Lancien, Antonín Procházka: Weak dentability index of spaces C([0,α]). [MATH-KMA 2008/279] Robert Deville, Antonín Procházka: Parametric variational principle and residuality. [MATH-KMA 2008/280] Michal Kraus: A note on the uniform approximation of continuous affine functions. [MATH-KMA 2008/281] Tomáš Bárta: Smooth solutions of Volterra equations via semigroups. [MATH-KMA 2008/282] Tomáš Bárta: Delayed quasilinear evolution equations with BV coefficients. [MATH-KMA 2008/283] Libor Veselý, Luděk Zajíček: On extensions of d.c. functions and convex functions. [MATH-KMA 2008/284] Ondřej Kalenda, Wies law Kubiś: The structure of Valdivia compact lines. [MATH-KMA 2008/285] Petr Holický: Borel classes of uniformizations of sets with large sections. [MATH-KMA 2008/286] Salvatore Leonardi, Jana Stará: Regularity results for the gradient of solutions of linear elliptic systems with V MO coefficients and L 1,λ data.
6 [MATH-KMA 2008/287] Andrea Cianchi, Luboš Pick: Optimal Gaussian Sobolev embeddings. [MATH-KMA 2008/288] Andrea Cianchi, Luboš Pick: An optimal endpoint trace embedding. [MATH-KMA 2008/289] Robert Černý, Stanislav Hencl, Jan Kolář: Integral functionals that are continuous with respect to the weak topology on W 1,p 0 (Ω). [MATH-KMA 2008/290] Jaroslav Lukeš, Luboš Pick, Dušan Pokorný: On geometric properties of the spaces L p(x).
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