Weak endpoint bounds for matrix weights

David Cruz-Uribe; Joshua Isralowitz; Kabe Moen; Sandra Pott; Israel P. Rivera-Rios

doi:10.4171/rmi/1237

Weak endpoint bounds for matrix weights

David Cruz-Uribe
, Joshua Isralowitz
, Kabe Moen
, Sandra Pott
, Israel P. Rivera-Rios

Mathematics and Statistics

University at Albany

University of Alabama
Lund University
Universidad Nacional del Sur

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

13 Scopus citations

Abstract

We prove quantitative, matrix weighted, endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderon-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class A1 introduced by M. Frazier and S. Roudenko. Even in the scalar case, our estimates are sharper than the results implicit in the literature.

Original language	English
Pages (from-to)	1513-1538
Number of pages	26
Journal	Revista Matematica Iberoamericana
Volume	37
Issue number	4
DOIs	https://doi.org/10.4171/rmi/1237
State	Published - 2021

Keywords

Calderon-Zygmund operators
Commutators
Matrix Ap
Matrix weights
Maximal operators
Sparse operators

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10.4171/rmi/1237

Cite this

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title = "Weak endpoint bounds for matrix weights",

abstract = "We prove quantitative, matrix weighted, endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderon-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class A1 introduced by M. Frazier and S. Roudenko. Even in the scalar case, our estimates are sharper than the results implicit in the literature.",

keywords = "Calderon-Zygmund operators, Commutators, Matrix Ap, Matrix weights, Maximal operators, Sparse operators",

author = "David Cruz-Uribe and Joshua Isralowitz and Kabe Moen and Sandra Pott and Rivera-Rios, \{Israel P.\}",

note = "Publisher Copyright: {\textcopyright} 2020 Real Sociedad Matematica Espanola. Published by EMS Press.",

year = "2021",

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language = "English",

volume = "37",

pages = "1513--1538",

journal = "Revista Matematica Iberoamericana",

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T1 - Weak endpoint bounds for matrix weights

AU - Cruz-Uribe, David

AU - Isralowitz, Joshua

AU - Moen, Kabe

AU - Pott, Sandra

AU - Rivera-Rios, Israel P.

PY - 2021

Y1 - 2021

N2 - We prove quantitative, matrix weighted, endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderon-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class A1 introduced by M. Frazier and S. Roudenko. Even in the scalar case, our estimates are sharper than the results implicit in the literature.

AB - We prove quantitative, matrix weighted, endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderon-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class A1 introduced by M. Frazier and S. Roudenko. Even in the scalar case, our estimates are sharper than the results implicit in the literature.

KW - Calderon-Zygmund operators

KW - Commutators

KW - Matrix Ap

KW - Matrix weights

KW - Maximal operators

KW - Sparse operators

UR - https://www.scopus.com/pages/publications/85107584568

U2 - 10.4171/rmi/1237

DO - 10.4171/rmi/1237

M3 - Article

SN - 0213-2230

VL - 37

SP - 1513

EP - 1538

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 4

ER -

Weak endpoint bounds for matrix weights

Abstract

Keywords

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