  We investigate the weighted bounds for multilinear maximal functions and
Calder\'on-Zygmund operators from $L^{p_1}(w_1)\times...\times L^{p_m}(w_m)$ to
$L^{p}(v_{\vec{w}})$, where $1<p_1,...,p_m<\infty$ with
$1/{p_1}+...+1/{p_m}=1/p$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weight. We
prove the sharp bound for the multilinear maximal function for all such
$p_1,..., p_m$ and prove the sharp bound for $m$-linear Calder\'on-Zymund
operators when $p\geq 1$.
