We study totally bounded sets in the spaces of variable integrability and summability. The full characterization of these sets is given. Furthermore, the Sudakov theorem in the setting of the mixed lebesgue sequence s...
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We study totally bounded sets in the spaces of variable integrability and summability. The full characterization of these sets is given. Furthermore, the Sudakov theorem in the setting of the mixed lebesgue sequence spaces is proven.
作者：
Fiorenza, A.Gogatishvili, A.Nekvinda, A.Rakotoson, J. M.Univ Napoli Federico II
Dipartimento Architettura Via Monteoliveto 2 I-80134 Naples Italy CNR
Ist Applicaz Calcolo Mauro Picone Sez Napoli Via Pietro Castellino 111 I-80131 Naples Italy Czech Acad Sci
Inst Math Zitna 25 Prague 11567 1 Czech Republic Czech Tech Univ
Fac Civil Engn Math Inst Thakurova 7 Prague 16629 6 Czech Republic Univ Poitiers
Lab Math & Applicat UMR CNRS 7348 SP2MI Bat H3Bd Marie & Pierre CurieTeleport 2 F-86962 Futuroscope France
Given the lebesgue space with variableexponent L-s(.)(Omega) whose norm is denoted by parallel *** to(s(.)), we show the following equivalence: lim(vertical bar E vertical bar -> 0) parallel to chi(E)parallel to(s...
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Given the lebesgue space with variableexponent L-s(.)(Omega) whose norm is denoted by parallel *** to(s(.)), we show the following equivalence: lim(vertical bar E vertical bar -> 0) parallel to chi(E)parallel to(s(.)) = 0 if and only if lim(p ->+infinity) 1/p [f(Omega)s(x)(p)dx](1/p) = 0, where chi(E) is the characteristic function of the measurable set E and vertical bar E vertical bar its lebesgue measure. We apply such results to characterize characterize compactness of some inclusions. (C) 2021 Elsevier Masson SAS. All rights reserved.
We study totally bounded sets in variablelebesguespaces. The full characterization of this kind of sets is given for the case of variablelebesgue space on metric measure spaces. Furthermore, the sufficient conditio...
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We study totally bounded sets in variablelebesguespaces. The full characterization of this kind of sets is given for the case of variablelebesgue space on metric measure spaces. Furthermore, the sufficient conditions for compactness are shown without assuming log-Holder continuity of the exponent.
We define a new class of functions of variable smoothness that are analytic in the unit disc and continuous in the closed disc. We construct the theory of the Nevanlinna outer-inner factorization, taking into account ...
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We define a new class of functions of variable smoothness that are analytic in the unit disc and continuous in the closed disc. We construct the theory of the Nevanlinna outer-inner factorization, taking into account the influence of the inner factor on the outer function, for functions of the new class.
In this paper, we investigate the description of complex interpolation between variable Morrey spaces. We show that the first complex interpolation between variable Morrey spaces equals to certain closed subspaces of ...
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In this paper, we investigate the description of complex interpolation between variable Morrey spaces. We show that the first complex interpolation between variable Morrey spaces equals to certain closed subspaces of variable Morrey spaces. In addition, we prove that the second complex interpolation of variable Morrey spaces coincides with their intermediate spaces. Our proof uses the characterization of the Calderon product between variable Morrey spaces. Our results cover complex interpoaltion of variablelebesguespaces and complex interpolation of (classical) Morrey spaces.
Our aim in this paper is to deal with integrability of maximal functions for generalized lebesgue spaces with variable exponent. Our exponent approaches 1 on some part of the domain, and hence the integrability depend...
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Our aim in this paper is to deal with integrability of maximal functions for generalized lebesgue spaces with variable exponent. Our exponent approaches 1 on some part of the domain, and hence the integrability depends on the shape of that part and the speed of the exponent approaching 1.
We address an open problem posed recently by Almeida and Hasto. They defined the spaces l(q)(.)(L-p(.)) of variable integrability and summability and showed that broken vertical bar broken vertical bar . |lq(.)(L-p(.)...
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We address an open problem posed recently by Almeida and Hasto. They defined the spaces l(q)(.)(L-p(.)) of variable integrability and summability and showed that broken vertical bar broken vertical bar . |lq(.)(L-p(.)) broken vertical bar broken vertical bar is a norm if q >= 1 is constant almost every-where or if 1/p(x)+1/q(x) = 1 for almost every x. R-n. Nevertheless, the natural conjecture (expressed also by Almeida and Hasto) is that the expression is a norm if p(x), q(x) = 1 almost everywhere. We show that broken vertical bar broken vertical *** vertical bar| ( q(.)(L-p(.)) broken vertical bar broken vertical bar is a norm if 1 <= q(x) <= p(x) for almost every x is an element of R-n. Furthermore, we construct an example of p(x) and q(x) with min(p(x), q(x)) >= 1 for every x. Rn such that the triangle inequality does not hold for broken vertical bar broken vertical bar. |broken vertical bar l(q)(.)(Lp(.)).
We apply the techniques of monotone and relative rearrangements to the nonrearrangernent invariant spaces L-P(center dot)(Omega) with variableexponent. In particular, we show that the maps u is an element of L-P(cent...
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We apply the techniques of monotone and relative rearrangements to the nonrearrangernent invariant spaces L-P(center dot)(Omega) with variableexponent. In particular, we show that the maps u is an element of L-P(center dot)(Omega) -> k(t)u(*) is an element of L-P(center dot) (0, means Omega) and u is an element of L-P(center dot)(Omega) -> u(*) is an element of L-P(center dot) (0, means Omega) are locally phi-Holderian (u(*) (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents. (C) 2007 Elsevier Masson SAS. All rights reserved.
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