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

TL;DR

This paper establishes sharp weighted bounds for multilinear fractional maximal operators with rough kernels, providing new estimates and bounds that improve understanding of their behavior in harmonic analysis.

Contribution

It introduces new weighted bounds for multilinear fractional maximal operators with rough kernels, including mixed $A_{(oldsymbol{P},q)}-A_ abla$ bounds and estimates for related integral operators.

Findings

Derived mixed $A_{(oldsymbol{P},q)}-A_ abla$ bounds.

Established $A_{oldsymbol{P}}$ type estimates.

Provided almost sharp bounds for multilinear fractional integral operators.

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