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Journal of Fourier Analysis and Applications

, Volume 20, Issue 4, pp 751–765 | Cite as

The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators

  • Kangwei Li
  • Kabe MoenEmail author
  • Wenchang Sun
Article

Abstract

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

Keywords

Multiple weights Multilinear maximal function Multilinear Calderón–Zygmund operators Weighted estimates 

Mathematics Subject Classification

42B20 42B25 47H60 

Notes

Acknowledgments

The authors thank Carlos Pérez for helping improve the quality of this article.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjin China
  2. 2.Department of MathematicsUniversity of AlabamaTuscaloosaUSA

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