Musielak-Orlicz-Sobolev spaces on metric measure spaces

Ohno, Takao   ; Shimomura, Tetsu

Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 435-474

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-015-0187-0

Classification : 31B15, 31E05, 46E35
Keywords: Sobolev space; metric measure space; Sobolev's inequality; Hajłasz-Sobolev space; Newton-Sobolev space; Musielak-Orlicz space; capacity; variable exponent

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