Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces

Abstract

Suppose $\vec{b}=(b_1,\cdots,b_m)\in (BMO)^m,$ $ I_{\alpha,m}^{{\Pi b}}$ is the iterated commutator of $\vec{b}$ and the $m$-linear multilinear fractional integral operator $I_{\alpha,m}$. The purpose of this paper is to discuss the boundedness properties of $I_{\alpha,m}$ and $I_{\alpha,m}^{{\Pi b}}$ on generalized Herz spaces with general Muckenhoupt weights.