Weighted Variable Sobolev Spaces and Capacity

摘要

We define weighted variable Sobolev capacity and discuss properties of capacity in the spaceW1,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 spaceW1,p(·)(ℝn,w). Also it is shown the relation between the Sobolev capacity and Bessel capacity.