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

By Kangwei Li, Kabe Moen, Wenchang Sun. Journal of Fourier Analysis and Applications, 2012

69 citations recorded by the source corpus.

We investigate the weighted bounds for multilinear maximal functions and Calderón–Zygmund operators from Lp1(w1)×⋯×Lpm(wm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p_1}(w_1)\times \cdots \times L^{p_m}(w_m)$$\end{document} to Lp(vw→)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}(v_{\vec {w}})$$\end{document}, where 1<p1,⋯,pm<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p_1,\cdots ,p_m<\infty $$\end{document} with 1/p1+⋯+1/pm=1/p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/{p_1}+\cdots +1/{p_m}=1/p$$\end{document} and w→\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vec {w}$$\end{document} is a multiple AP→\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_1,\ldots , p_m$$\end{document} and prove the sharp bound for m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document}-linear Calderón–Zymund operators when p≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\ge 1$$\end{document}.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a645f8f7595be92670005013fcc5b4f0f96b756b

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Citations in the corpus

Uniform sparse domination of singular integrals via dyadic shifts (2016, background): “See [19] for a self-contained argument deducing (1.”
Extrapolation for multilinear Muckenhoupt classes and applications (2018, background): “To proceed we follow an argument in [15], see also [29], which in turn is a bilinear extension of the linear case proof in [13].”
A pointwise estimate for positive dyadic shifts and some applications (2014, methodology): “The same theorem was proven in [19] but with the additional hypothesis that p had to be at least 1.”
Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, background): “One can also follow the maximal function trick used in [9] and then utilize the result in [22].”