Weighted estimates for fractional integrals with Distances to Bounded Median Porous Sets and applications to Hardy--Sobolev Inequalities
Abstract
Weighted estimates for the fractional integral operator Iα are established and subsequently applied to derive corresponding Hardy--Sobolev inequalities. The weights are constructed from distance functions to bounded median porous sets and possess mixed homogeneity, which enables us to extend earlier results obtained for porous sets to a significantly broader class of geometries.
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