Musielak-Orlicz-Sobolev spaces on metric measure spaces

Title:

Musielak-Orlicz-Sobolev spaces on metric measure spaces

Creator:

Ohno, Takao and Shimomura, Tetsu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3356ca43-dd8f-423b-92fd-444debee4ba3
uuid:3356ca43-dd8f-423b-92fd-444debee4ba3
issn:0011-4642

Subject:

matematika, mathematics, Sobolev space, metric measure space, Sobolev’s inequality, Hajłasz-Sobolev space, Newton-Sobolev space, Musielak-Orlicz space, capacity, variable exponent, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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., Takao Ohno, Tetsu Shimomura., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

435-474

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:2

Harvested from:

CDK

Metadata only:

false