Multilinear fractional Calder\'{o}n-Zygmund operators with Dini type kernel

TL;DR

This paper studies the boundedness and endpoint estimates of multilinear fractional Calderón-Zygmund operators with Dini-type kernels, extending understanding of their behavior on variable exponent Lebesgue spaces.

Contribution

It establishes endpoint weak-type estimates and boundedness properties of multilinear fractional operators with Dini regularity kernels, including on variable exponent Lebesgue spaces.

Findings

Established endpoint weak-type estimates for multilinear fractional operators.

Proved boundedness on variable exponent Lebesgue spaces.

Extended the theory of Calderón-Zygmund operators with Dini kernels.

Abstract

In this paper, the main purpose is to consider a number of results concerning boundedness of multilinear fractional Calder\'{o}n-Zygmund operators with kernels of mild regularity. Let $T_{\alpha}$ be a multilinear fractional Calder\'{o}n-Zygmund operators of type $\omega(t)$ with $\omega$ being nondecreasing and $\omega \in \text{Dini}(1)$. The end-point weak-type estimates for multilinear operator $T_{\alpha}$ are obtained. Moreover, some boundedness properties of the multilinear fractional operators are also established on variable exponent Lebesgue spaces.