- Tytuł:
- Musielak−Orlicz−Sobolev spaces on arbitrary metrique space
- Autorzy:
-
Youssef, Akdim
Aissaoui, Noureddine
Cherif Hassib, My - Powiązania:
- https://bibliotekanauki.pl/articles/745903.pdf
- Data publikacji:
- 2016
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Metric measure space
Musielak−Orlicz−Sobolev spaces
capacity - Opis:
- 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.
- Źródło:
-
Commentationes Mathematicae; 2016, 56, 2
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł