Multilinear $\theta$-type Calder\'on--Zygmund operators and commutators on products of weighted Morrey spaces

TL;DR

This paper investigates the boundedness of multilinear $ heta$-type Calderón--Zygmund operators and their commutators on products of weighted Morrey spaces, providing new estimates and endpoint results.

Contribution

It establishes strong and weak type bounds for these operators and their commutators on weighted Morrey spaces, extending previous results to multilinear and endpoint cases.

Findings

Proved strong and weak type estimates for $T_ heta$ on weighted Morrey spaces.

Established boundedness of commutators and iterated commutators.

Derived weak endpoint estimates involving BMO functions.

Abstract

In this paper, we consider the boundedness properties of multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in the literature. First, we prove strong type and weak type estimates for multilinear $\theta$-type Calder\'on--Zygmund operators on products of weighted Morrey spaces with multiple weights. Then we discuss strong type estimates for both multilinear commutators and iterated commutators of $T_\theta$ on products of these spaces with multiple weights. Furthermore, the weak end-point estimates for commutators of $T_\theta$ and pointwise multiplication with functions in bounded mean oscillation are established too.