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arXiv · 1212.1054

The sharp weighted bound for multilinear maximal functions and Calder\'{o}n-Zygmund operators

Kangwei Li·Kabe Moen·Wenchang Sun
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Abstract

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 $p\geq 1$.

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Kangwei Li, Kabe Moen, Wenchang Sun. 2012-12-05. The sharp weighted bound for multilinear maximal functions and Calder\'{o}n-Zygmund operators. https://arxiv.org/abs/1212.1054

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