Weighted Boundedness of Commutators of Fractional Hardy Operators with Besov-Lipschitz Functions

Abstract

In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by $H^{\alpha}_b$, is bounded from $L^p_{x^\gamma} (R_+)$ to $L^q_{x^\delta} (R_+)$ with the bound explicitly worked out.