  In this paper, we prove that if a multilinear operator $\mathcal{T}$ and its
multilinear commutator $\mathcal{T}_{\Sigma\vec{b}}$ and iterated commutator
$\mathcal{T}_{\Pi\vec{b}}$ for $\vec{b}\in(\mathbb{R}^n)^m$ are bounded on
product weighted Lebesgue space, then $\mathcal{T}$,
$\mathcal{T}_{\Sigma\vec{b}}$ and $\mathcal{T}_{\Pi\vec{b}}$ are also bounded
on product weighted Amalgam space. As its applications, we show that
multilinear Littlewood-Paley functions and multilinear Marcinkiewicz integral
functions with kernels of convolution type and non-convolution type, and their
multilinear commutators and iterated commutators are bounded on product
weighted Amalgam space. We also consider multilinear fractional type integral
operators and their commutators' behaviors on weighted amalgam space. In order
to deal with the endpoint case, we introduce the amalgam-Campanato space and
show that fractional integral integral operator are bounded operators from
product amalgam space to amalgam-Campanato space. What should point out is that
even if in the linear case, our results for fractional integral operator are
also new.
