Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
type: Item
instance of: scholarly article
title: Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
zbMATH Open document ID: 1085.31005
author: Yoshihiro Mizuta
author: Tetsu Shimomura
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-10-17T00:00:00Z
review text: The authors study maximal functions in a variable \(L^{p(\cdot)}\)-space. They prove (weaker) boundedness of the maximal function under weaker assumptions on the exponent function \(p(\cdot)\) than in \textit{D. Cruz-Uribe, A. Firorenza} and \textit{C. J. Neugebauer} [Ann. Acad. Sci. Fenn., Math. 28, No. 1, 223--238 (2003; Zbl 1037.42023)]. As an application of the boundedness of the maximal function they show Sobolev's inequality for Riesz potentials with variable exponent.
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 2214831
zbMATH Keywords: Riesz potentials
zbMATH Keywords: maximal functions
zbMATH Keywords: Sobolev's imbedding theorem of variable exponents
zbMATH Keywords: boundedness
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.02.046
OpenAlex ID: W2048356603
cites work: Q4458796
cites work: Maximal function on generalized Lebesgue spaces L^p(⋅)
cites work: Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
cites work: Q4797974
cites work: On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
cites work: Sobolev embeddings for Riesz potential space of variable exponent
cites work: Q5483199
cites work: Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator
cites work: On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent
cites work: Q4021390
cites work: Q3437163
cites work: Orlicz spaces and modular spaces
cites work: Über konjugierte Exponentenfolgen
cites work: An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
cites work: Electrorheological fluids: Modeling and mathematical theory
cites work: Convolution and potential type operators inLp(x)(Rn)
DOI: 10.1016/J.JMAA.2005.02.046
Recommended article: Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent
Recommended article: On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent
Recommended article: Q5167049
Recommended article: Q5401299
Recommended article: Sur l'inégalité logarithmique de Sobolev
Recommended article: A generalization of a logarithmic Sobolev inequality to the Hölder class
Recommended article: Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces
Recommended article: Logarithmic Sobolev inequalities and exponential integrability
Recommended article: The q-logarithmic Sobolev inequality in infinite dimensions
Recommended article: Q5747317
description: scientific article