Weighted Variable Sobolev Spaces and Capacity

We define weighted variable Sobolev capacity and discuss properties of capacity in the space W-1,W-p(.) (R-n,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 W-1,W-p(.) (R-n,w). Also it is shown the relation between the Sobolev capacity and Bessel capacity.