Weighted Variable Sobolev Spaces and Capacity

By I. Aydın. 2012

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We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). Also it is shown the relation between the Sobolev capacity and Bessel capacity.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/46e649f7cbe4274ce53a48dd809fd1566d421759