Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators

2012/11/21 by Wendolín Damián, Andrei K. Lerner, Damián, Wendolín +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1211.5115

openalex publication_date 2012/11/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function \Mm introduced in \citeLOPTT and for multilinear Calderón-Zygmund operators. In particular we obtain a sharp mixed "A_p-A_∞" bound for \Mm, some partial results related to a Buckley-type estimate for \Mm, and a sufficient condition for the boundedness of \Mm between weighted L^p spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón-Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work. Then we obtain a multilinear version of the "A₂ conjecture". Several open problems are posed.

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