Musielak−Orlicz−Sobolev spaces on arbitrary metrique space

@article{AkdimYoussef2016,
abstract = {In this article we define Musielak−Orlicz−Sobolev spaces on arbitrary metric spaces with finite diameter and equipped with finite, positive Borel regular outer measure. We employ a Hajlasz definition, which uses a pointwise maximal inequality. We prove that these spaces are Banach, that the Poincaré inequality holds, and that the Lipschitz functions are dense. We develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. As an application, we prove that each Musielak−Orlicz−Sobolev function has a quasi-continuous representative.},
author = {Akdim Youssef, Noureddine Aissaoui, My Cherif Hassib},
journal = {Commentationes Mathematicae},
keywords = {Metric measure space; Musielak−Orlicz−Sobolev spaces; capacity},
language = {eng},
number = {2},
pages = {null},
title = {Musielak−Orlicz−Sobolev spaces on arbitrary metrique space},
url = {http://eudml.org/doc/292379},
volume = {56},
year = {2016},
}

TY - JOUR
AU - Akdim Youssef
AU - Noureddine Aissaoui
AU - My Cherif Hassib
TI - Musielak−Orlicz−Sobolev spaces on arbitrary metrique space
JO - Commentationes Mathematicae
PY - 2016
VL - 56
IS - 2
SP - null
AB - In this article we define Musielak−Orlicz−Sobolev spaces on arbitrary metric spaces with finite diameter and equipped with finite, positive Borel regular outer measure. We employ a Hajlasz definition, which uses a pointwise maximal inequality. We prove that these spaces are Banach, that the Poincaré inequality holds, and that the Lipschitz functions are dense. We develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. As an application, we prove that each Musielak−Orlicz−Sobolev function has a quasi-continuous representative.
LA - eng
KW - Metric measure space; Musielak−Orlicz−Sobolev spaces; capacity
UR - http://eudml.org/doc/292379
ER -