Sharp Weighted Bounds for Multilinear fractional Maximal type Operators with Rough Kernels

Abstract

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators ${\mathcal{M}}_{\Omega ,\alpha }$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_{\infty }$ bound and a $A_{\vec{P}}$ type estimate for ${\mathcal{M}}_{\Omega ,\alpha }$. As an application, we give an almost sharp estimate for the multilinear fractional integral operator with rough kernels ${\mathcal{I}}_{\Omega ,\alpha }$.

18 pages