A Study of One-Sided Singular Integral and Function Space via Reproducing Formula

Zunwei Fu; Xianming Hou; Ming Yi Lee; Ji Li

doi:10.1007/s12220-023-01340-8

A Study of One-Sided Singular Integral and Function Space via Reproducing Formula

Zunwei Fu
, Xianming Hou
, Ming Yi Lee
, Ji Li

Department of Mathematics

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

19 Scopus citations

Abstract

In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S-square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.

Original language	English
Article number	289
Journal	Journal of Geometric Analysis
Volume	33
Issue number	9
DOIs	https://doi.org/10.1007/s12220-023-01340-8
State	Published - Sep 2023

Keywords

Atomic decomposition
Calderón reproducing formula
Commutator
One-sided Hardy space
One-sided Triebel–Lizorkin space

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10.1007/s12220-023-01340-8

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abstract = "In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S-square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.",

keywords = "Atomic decomposition, Calder{\'o}n reproducing formula, Commutator, One-sided Hardy space, One-sided Triebel–Lizorkin space",

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AU - Hou, Xianming

AU - Lee, Ming Yi

AU - Li, Ji

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Y1 - 2023/9

N2 - In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S-square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.

AB - In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S-square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.

KW - Atomic decomposition

KW - Calderón reproducing formula

KW - Commutator

KW - One-sided Hardy space

KW - One-sided Triebel–Lizorkin space

UR - https://www.scopus.com/pages/publications/85163742117

U2 - 10.1007/s12220-023-01340-8

DO - 10.1007/s12220-023-01340-8

M3 - 期刊論文

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 9

M1 - 289

ER -

A Study of One-Sided Singular Integral and Function Space via Reproducing Formula

Abstract

Keywords

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