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Weighted Variable Sobolev Spaces and Capacity

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

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