Translator Disclaimer
Open Access
VOL. 44 | 2006 Maximal functions, Riesz potentials and Sobolev's inequality in generalized Lebesgue spaces
Yoshihiro Mizuta, Tetsu Shimomura

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

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

PROCEEDINGS ARTICLE
27 PAGES


SHARE
Back to Top