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

^*Corresponding author for this work

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

13 Citations (Scopus)

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
Pages (from-to)	1-34
Number of pages	34
Journal	Journal of Geometric Analysis
Volume	33
Issue number	9
DOIs	https://doi.org/10.1007/s12220-023-01340-8
Publication status	Published - Sept 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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title = "A Study of one-sided singular integral and function space via reproducing formula",

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",

author = "Zunwei Fu and Xianming Hou and Ming-Yi Lee and Ji Li",

year = "2023",

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doi = "10.1007/s12220-023-01340-8",

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AU - Fu, Zunwei

AU - Hou, Xianming

AU - Lee, Ming-Yi

AU - Li, Ji

PY - 2023/9

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 - http://www.scopus.com/inward/record.url?scp=85163742117&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP220100285

U2 - 10.1007/s12220-023-01340-8

DO - 10.1007/s12220-023-01340-8

M3 - Article

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EP - 34

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

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DP22: Harmonic analysis of Laplacians in curved spaces

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A Study of one-sided singular integral and function space via reproducing formula

Abstract

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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