Weighted estimates for generalized Riesz potentials

TL;DR

This paper derives weighted estimates for generalized Riesz potentials, expanding understanding of fractional operators within weighted Sobolev and Lebesgue spaces.

Contribution

It provides new weighted $H^{p}_{w} - L^{q}_{w^{q/p}}$ estimates for fractional operators, advancing the theory of these operators in weighted function spaces.

Findings

Established weighted estimates for fractional operators

Extended classical results to weighted Sobolev and Lebesgue spaces

Enhanced understanding of fractional operator behavior under weights

Abstract

We obtain $H^{p}_{w} - L^{q}_{w^{q/p}}$ estimates for certain fractional operators.