An operator-valued T1 theory for symmetric CZOs

Guixiang Hong; Honghai Liu; Tao Mei

doi:10.1016/j.jfa.2019.108420

An operator-valued T1 theory for symmetric CZOs

Guixiang Hong
, Honghai Liu^*
, Tao Mei

^*Corresponding author for this work

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

9 Scopus citations

Abstract

We provide a natural BMO-criterion for the L₂-boundedness of Calderón-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L₂-boundedness of the commutators [R_j,b] whenever b belongs to the Bourgain's vector-valued BMO space, where R_j is the j-th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.

Original language	English
Article number	108420
Journal	Journal of Functional Analysis
Volume	278
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2019.108420
State	Published - 15 Apr 2020
Externally published	Yes

Keywords

Calderon-Zygmund operator
Noncommuting martingale transforms
Operator-valued kernel
T1 theorem

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10.1016/j.jfa.2019.108420

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title = "An operator-valued T1 theory for symmetric CZOs",

abstract = "We provide a natural BMO-criterion for the L2-boundedness of Calder{\'o}n-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L2-boundedness of the commutators [Rj,b] whenever b belongs to the Bourgain's vector-valued BMO space, where Rj is the j-th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.",

keywords = "Calderon-Zygmund operator, Noncommuting martingale transforms, Operator-valued kernel, T1 theorem",

author = "Guixiang Hong and Honghai Liu and Tao Mei",

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year = "2020",

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T1 - An operator-valued T1 theory for symmetric CZOs

AU - Hong, Guixiang

AU - Liu, Honghai

AU - Mei, Tao

PY - 2020/4/15

Y1 - 2020/4/15

N2 - We provide a natural BMO-criterion for the L2-boundedness of Calderón-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L2-boundedness of the commutators [Rj,b] whenever b belongs to the Bourgain's vector-valued BMO space, where Rj is the j-th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.

AB - We provide a natural BMO-criterion for the L2-boundedness of Calderón-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix, we give a proof of the L2-boundedness of the commutators [Rj,b] whenever b belongs to the Bourgain's vector-valued BMO space, where Rj is the j-th Riesz transform. A common ingredient is the operator-valued Haar multiplier studied by Blasco and Pott.

KW - Calderon-Zygmund operator

KW - Noncommuting martingale transforms

KW - Operator-valued kernel

KW - T1 theorem

UR - https://www.scopus.com/pages/publications/85076552194

U2 - 10.1016/j.jfa.2019.108420

DO - 10.1016/j.jfa.2019.108420

M3 - 文章

AN - SCOPUS:85076552194

SN - 0022-1236

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

M1 - 108420

ER -

An operator-valued T1 theory for symmetric CZOs

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Keywords

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