Musielak-Orlicz-Sobolev spaces on metric measure spaces

Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 435-474
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ohno, Takao, and Shimomura, Tetsu. "Musielak-Orlicz-Sobolev spaces on metric measure spaces." Czechoslovak Mathematical Journal 65.2 (2015): 435-474. <http://eudml.org/doc/270122>.

@article{Ohno2015,
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.},
author = {Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sobolev space; metric measure space; Sobolev's inequality; Hajłasz-Sobolev space; Newton-Sobolev space; Musielak-Orlicz space; capacity; variable exponent},
language = {eng},
number = {2},
pages = {435-474},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Musielak-Orlicz-Sobolev spaces on metric measure spaces},
url = {http://eudml.org/doc/270122},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Musielak-Orlicz-Sobolev spaces on metric measure spaces
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 435
EP - 474
AB - 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.
LA - eng
KW - Sobolev space; metric measure space; Sobolev's inequality; Hajłasz-Sobolev space; Newton-Sobolev space; Musielak-Orlicz space; capacity; variable exponent
UR - http://eudml.org/doc/270122
ER -

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