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

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.