Musielak−Orlicz−Sobolev spaces on arbitrary metrique space

• Autorzy: Akdim Youssef , Noureddine Aissaoui , My Cherif Hassib
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Metric measure space; Musielak−Orlicz−Sobolev spaces; capacity

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: 56
• Numer: 2

Daty

wydano

2016

online

2017-02-13

Twórcy

autor

Akdim Youssef

autor

Noureddine Aissaoui

autor

My Cherif Hassib

Identyfikatory

DOI

10.14708/cm.v56i2.825