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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).
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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