Musielak-Orlicz-Sobolev spaces on metric measure spaces

Czechoslovak Mathematical Journal

Tetsu Shimomura¹  Takao Ohno² 

[1] Department of Mathematics, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama Higashi-Hiroshima 739-8524, Japan;Faculty of Education and Welfare Science, ita University, 700 Dannoharu ita-city 870-1192, Japan

关键词: Sobolev space;    metric measure space;    Sobolev's inequality;    Hajł;    asz-Sobolev space;    Newton-Sobolev space;    Musielak-Orlicz space;    capacity;    variable exponent;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown