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

University of Seville
University of the Basque Country
Ikerbasque Basque Foundation for Science

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

38 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

Calderón–Zygmund theory
Multilinear maximal operator
Sharp weighted bounds

Access to Document

10.1007/s00041-014-9364-z

Cite this

@article{78a870f50aff49fe87d7493e92afcdd9,

title = "Sharp Weighted Bounds for Multilinear Maximal Functions and Calder{\'o}n{\textendash}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{\textendash}1264, 2009) and for multilinear Calder{\'o}n{\textendash}Zygmund operators. In particular we obtain a sharp mixed {\textquotedblleft}Ap-A∞{\textquotedblright} 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{\textendash}Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work (Lerner, J Anal Math 121:141{\textendash}161, 2013). Then we obtain a multilinear version of the {\textquotedblleft}A2 conjecture{\textquotedblright}. Several open problems are posed.",

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

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

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2015",

month = feb,

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

language = "אנגלית",

volume = "21",

pages = "161--181",

journal = "Journal of Fourier Analysis and Applications",

issn = "1069-5869",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

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

KW - Multilinear maximal operator

KW - Sharp weighted bounds

UR - https://www.scopus.com/pages/publications/84943589324

U2 - 10.1007/s00041-014-9364-z

DO - 10.1007/s00041-014-9364-z

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84943589324

SN - 1069-5869

VL - 21

SP - 161

EP - 181

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this