Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators

Wendolín Damián; Andrei K. Lerner; Carlos Pérez

doi:10.1007/s00041-014-9364-z

Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators

Wendolín Damián, Andrei K. Lerner, Carlos Pérez

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv Math 220:1222–1264, 2009) and for multilinear Calderón–Zygmund operators. In particular we obtain a sharp mixed “A_p-A_∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M 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 (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A₂ conjecture”. Several open problems are posed.

Original language	English
Pages (from-to)	161-181
Number of pages	21
Journal	Journal of Fourier Analysis and Applications
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s00041-014-9364-z
State	Published - Feb 2015

Keywords

Calderón–Zygmund theory
Multilinear maximal operator
Sharp weighted bounds

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics
Applied Mathematics

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10.1007/s00041-014-9364-z

Cite this

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title = "Sharp Weighted Bounds for Multilinear Maximal Functions and Calder{\'o}n–Zygmund Operators",

abstract = "In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv Math 220:1222–1264, 2009) and for multilinear Calder{\'o}n–Zygmund operators. In particular we obtain a sharp mixed “Ap-A∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M between weighted Lp spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calder{\'o}n–Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.",

keywords = "Calder{\'o}n–Zygmund theory, Multilinear maximal operator, Sharp weighted bounds",

author = "Wendol{\'i}n Dami{\'a}n and Lerner, \{Andrei K.\} and Carlos P{\'e}rez",

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year = "2015",

month = feb,

doi = "10.1007/s00041-014-9364-z",

language = "الإنجليزيّة",

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T1 - Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators

AU - Damián, Wendolín

AU - Lerner, Andrei K.

AU - Pérez, Carlos

PY - 2015/2

Y1 - 2015/2

N2 - In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv Math 220:1222–1264, 2009) and for multilinear Calderón–Zygmund operators. In particular we obtain a sharp mixed “Ap-A∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M between weighted Lp 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 (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.

AB - In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in Lerner et al. (Adv Math 220:1222–1264, 2009) and for multilinear Calderón–Zygmund operators. In particular we obtain a sharp mixed “Ap-A∞” bound for M, some partial results related to a Buckley-type estimate for M, and a sufficient condition for the boundedness of M between weighted Lp 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 (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “A2 conjecture”. Several open problems are posed.

KW - Calderón–Zygmund theory

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KW - Sharp weighted bounds

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DO - 10.1007/s00041-014-9364-z

M3 - مقالة

SN - 1069-5869

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JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

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ER -

Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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