Multilinear $\theta$-type Calderon--Zygmund operators and their commutators on products of weighted amalgam spaces

TL;DR

This paper introduces new weighted amalgam spaces and establishes boundedness and endpoint estimates for multilinear $ heta$-type Calderon--Zygmund operators and their commutators on these spaces.

Contribution

It develops new classes of weighted amalgam spaces and provides the first boundedness and endpoint estimates for multilinear $ heta$-type Calderon--Zygmund operators and their commutators.

Findings

Established strong and weak type estimates for $T_ heta$ on product spaces.

Proved endpoint estimates for multilinear commutators and iterated commutators.

Extended the theory to include pointwise multiplication with BMO functions.

Abstract

In this paper, we first introduce several new classes of weighted amalgam spaces. Then we discuss both strong type and weak type estimates for certain multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in the literature on products of these spaces with multiple weights. Furthermore, the strong type and weak end-point estimates for both multilinear commutators and iterated commutators of $T_\theta$ and pointwise multiplication with BMO functions are established as well.