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 $\mathcal{I}{\Omega,\alpha}$.