The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators

Abstract

We investigate the weighted bounds for multilinear maximal functions and Calderón-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 Calderón-Zymund operators when $p\ge 1$.

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• $A_p$-$A_{\infty }$ estimates for multilinear maximal and sparse operators