A noncommutative weak type (1,1) estimate for a square function from ergodic theory

Guixiang Hong; Bang Xu

doi:10.1016/j.jfa.2021.108959

A noncommutative weak type (1,1) estimate for a square function from ergodic theory

Guixiang Hong
, Bang Xu^*

^*Corresponding author for this work

Wuhan University

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

12 Scopus citations

Abstract

In this paper, we investigate the boundedness of a square function operator from ergodic theory acting on noncommutative L_p-spaces. The main result is a weak type (1,1) estimate of this operator. We also show the (L_∞,BMO) estimate, and thus all the strong type (L_p,L_p) estimates by interpolation. The main new difficulty lies in the fact that the kernel of this square function operator does not enjoy any regularity, while the Lipschitz regularity assumption is crucial in showing such endpoint estimates for the noncommutative Calderón-Zygmund singular integrals.

Original language	English
Article number	108959
Journal	Journal of Functional Analysis
Volume	280
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2021.108959
State	Published - 1 May 2021
Externally published	Yes

Keywords

Almost orthogonality principle
Calderón-Zygmund decomposition
Noncommutative L-space
Pseudo-localization

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10.1016/j.jfa.2021.108959

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title = "A noncommutative weak type (1,1) estimate for a square function from ergodic theory",

abstract = "In this paper, we investigate the boundedness of a square function operator from ergodic theory acting on noncommutative Lp-spaces. The main result is a weak type (1,1) estimate of this operator. We also show the (L∞,BMO) estimate, and thus all the strong type (Lp,Lp) estimates by interpolation. The main new difficulty lies in the fact that the kernel of this square function operator does not enjoy any regularity, while the Lipschitz regularity assumption is crucial in showing such endpoint estimates for the noncommutative Calder{\'o}n-Zygmund singular integrals.",

keywords = "Almost orthogonality principle, Calder{\'o}n-Zygmund decomposition, Noncommutative L-space, Pseudo-localization",

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AU - Hong, Guixiang

AU - Xu, Bang

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N2 - In this paper, we investigate the boundedness of a square function operator from ergodic theory acting on noncommutative Lp-spaces. The main result is a weak type (1,1) estimate of this operator. We also show the (L∞,BMO) estimate, and thus all the strong type (Lp,Lp) estimates by interpolation. The main new difficulty lies in the fact that the kernel of this square function operator does not enjoy any regularity, while the Lipschitz regularity assumption is crucial in showing such endpoint estimates for the noncommutative Calderón-Zygmund singular integrals.

AB - In this paper, we investigate the boundedness of a square function operator from ergodic theory acting on noncommutative Lp-spaces. The main result is a weak type (1,1) estimate of this operator. We also show the (L∞,BMO) estimate, and thus all the strong type (Lp,Lp) estimates by interpolation. The main new difficulty lies in the fact that the kernel of this square function operator does not enjoy any regularity, while the Lipschitz regularity assumption is crucial in showing such endpoint estimates for the noncommutative Calderón-Zygmund singular integrals.

KW - Almost orthogonality principle

KW - Calderón-Zygmund decomposition

KW - Noncommutative L-space

KW - Pseudo-localization

UR - https://www.scopus.com/pages/publications/85101300529

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DO - 10.1016/j.jfa.2021.108959

M3 - 文章

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SN - 0022-1236

VL - 280

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

M1 - 108959

ER -

A noncommutative weak type (1,1) estimate for a square function from ergodic theory

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Keywords

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