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Capacitary type estimates in strongly nonlinear potential theory and applications.

Noureddine Aissaoui — 2001

Revista Matemática Complutense

In this article a general result on smooth truncation of Riesz and Bessel potentials in Orlicz-Sobolev spaces is given and a capacitary type estimate is presented. We construct also a space of quasicontinuous functions and an alternative characterization of this space and a description of its dual are established. For the Riesz kernel R, we prove that operators of strong type (A, A), are also of capacitaries strong and weak types (m,A).

Musielak−Orlicz−Sobolev spaces on arbitrary metrique space

Akdim Youssef;  Noureddine Aissaoui;  My Cherif Hassib — 2016

Commentationes Mathematicae

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,...

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