Commutators of multilinear Calder\'on-Zygmund operators with kernels of Dini's type and applications

TL;DR

This paper studies the boundedness of iterated commutators of multilinear Calderón-Zygmund operators with Dini-type kernels, providing new weighted estimates and applications to paraproducts and pseudo-differential operators.

Contribution

It introduces weighted endpoint estimates and boundedness results for commutators of multilinear Calderón-Zygmund operators with Dini-type kernels, extending previous work to variable exponent spaces and applications.

Findings

Established weighted strong and weak endpoint estimates for commutators.

Proved boundedness on weighted variable exponent Lebesgue spaces.

Derived applications to paraproducts and bilinear pseudo-differential operators.

Abstract

Let $T$ be a multilinear Calder\'on-Zygmund operator of type $\omega$ with $\omega(t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{\Pi\vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The weighted strong and weak $L(\log{L})$-type endpoint estimates for $T_{\Pi\vec{b}}$ with multiple weights are established. Some boundedness properties on weighted variable exponent Lebesgue spaces are also obtained. As applications, multiple weighted estimates for iterated commutators of paraproducts and bilinear pseudo-differential operators with mild regularity are given.