Musielak-Orlicz-Sobolev spaces on metric measure spaces.

Autor:	Ohno, Takao
Další autoři:	Shimomura, Tetsu
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles Sobolev space metric measure space Sobolev’s inequality Hajłasz-Sobolev space Newton-Sobolev space Musielak-Orlicz space capacity variable exponent
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	Abstract: Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood maximal operator, we establish a generalization of Sobolev’s inequality for Sobolev functions in Musielak-Orlicz-Hajłasz-Sobolev spaces.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Online Access Full text from SpringerLink