Abstract
Our aim in this paper is to deal with the boundedness of maximal functions in Lebesgue spaces with variable exponent. Our result extends the recent work of Diening [4], Cruz-Uribe, Fiorenza and Neugebauer [3] and the authors [8]. As an application of the boundedness of maximal functions, we show Sobolev's inequality for Riesz potentials with variable exponent.
Information
Published: 1 January 2006
First available in Project Euclid: 16 December 2018
zbMATH: 1125.31001
MathSciNet: MR2277839
Digital Object Identifier: 10.2969/aspm/04410255
Subjects:
Primary:
31B15
,
42B25
,
46E30
Keywords:
Hardy's inequality
,
Lebesgue spaces with variable exponent
,
maximal functions
,
Riesz potentials
,
Sobolev's inequality
Rights: Copyright © 2006 Mathematical Society of Japan
