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

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.