Geodesic
Musielak−Orlicz−Sobolev spaces on arbitrary metrique space
Commentationes Mathematicae, Tome 56 (2016) no. 2, p. 169−183.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/cm.v56i2.825
Classification : 46E35, 31B15, 46E30, 42B25, 28A80
Mots-clés : Metric measure space, Musielak−Orlicz−Sobolev spaces, capacity 
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Akdim Youssef; Noureddine Aissaoui; My Cherif Hassib. Musielak−Orlicz−Sobolev spaces on arbitrary metrique space. Commentationes Mathematicae, Tome 56 (2016) no. 2, p.  169−183. doi : 10.14708/cm.v56i2.825. http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i2.825/

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