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

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 resul...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 9
Main Authors Fu, Zunwei, Hou, Xianming, Lee, Ming-Yi, Li, Ji
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2023
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Commutators
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Function space
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Operators (mathematics)
Primary 42B20
Commutator
42B35
42B30
Calderón reproducing formula
One-sided Hardy space
One-sided Triebel–Lizorkin space
Secondary 42B25
Atomic decomposition
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01340-8