We investigate the weighted bounds for multilinear maximal functions and Calderón–Zygmund operators from Lp1(w1)×⋯×Lpm(wm)\documentclass[12pt]{minimal}
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\begin{document}$$L^{p_1}(w_1)\times \cdots \times L^{p_m}(w_m)$$\end{document} to Lp(vw→)\documentclass[12pt]{minimal}
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\begin{document}$$L^{p}(v_{\vec {w}})$$\end{document}, where 1<p1,⋯,pm<∞\documentclass[12pt]{minimal}
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\begin{document}$$1<p_1,\cdots ,p_m<\infty $$\end{document} with 1/p1+⋯+1/pm=1/p\documentclass[12pt]{minimal}
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\begin{document}$$1/{p_1}+\cdots +1/{p_m}=1/p$$\end{document} and w→\documentclass[12pt]{minimal}
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\begin{document}$$\vec {w}$$\end{document} is a multiple AP→\documentclass[12pt]{minimal}
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\begin{document}$$A_{\vec {P}}$$\end{document} weight. We prove the sharp bound for the multilinear maximal function for all such p1,…,pm\documentclass[12pt]{minimal}
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\begin{document}$$p_1,\ldots , p_m$$\end{document} and prove the sharp bound for m\documentclass[12pt]{minimal}
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\begin{document}$$m$$\end{document}-linear Calderón–Zymund operators when p≥1\documentclass[12pt]{minimal}
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\begin{document}$$p\ge 1$$\end{document}.
