Maximal functions, Riesz potentials and Sobolev's inequality in generalized Lebesgue spaces

Mizuta, Yoshihiro; Shimomura, Tetsu

doi:10.2969/aspm/04410255

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

Adv. Stud. Pure Math., 2006: 255-281 (2006) DOI: 10.2969/aspm/04410255

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.