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

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