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In this paper, we investigate the weighted vector-valued bounds for a classof multilinear singular integral operators, and its commutators, from$L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\timesL^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to$L^{p}(l^q;\,\mathbb{R}^n,\nu_{\vec{w}})$, with $p_1,\dots,p_m\in (1,\,\infty)$and $1/p=1/p_1+\dots+1/p_m$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weights.Our argument also leads to the weighted weak type endpoint estimates for thecommutators.

Weighted vector-valued bounds for a class of multilinear singular integral operators