Two-Weight Inequalities for Commutators with Fractional Integral Operators

Abstract

In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $\mu ,\lambda \in A_{p,q}$ and $\alpha /n+1/q=1/p$, the norm $\Vert [b,I_{\alpha }]:L^p({\mu }^p)\to L^q({\lambda }^q)\Vert$ is equivalent to the norm of $b$ in the weighted BMO space $BMO(\nu )$, where $\nu =\mu {\lambda }^{-1}$. This work extends some of the results on this topic existing in the literature, and continues a line of investigation which was initiated by Bloom in 1985 and was recently developed further by the first author, Lacey, and Wick.

References in corpus (2)

• Commutators in the Two-Weight Setting
• Characterizations of BMO through commutators of bilinear singular integral operators

Cited by in corpus (1)

• A Revisit on Commutators of linear and bilinear Fractional Integral Operator