Singular integral and local Hardy spaces in Dunkl setting

Yanchang Han; Yongsheng Han; Ji Li; Chaoqiang Tan

doi:10.4208/ata.2025.deng90.01

Singular integral and local Hardy spaces in Dunkl setting

Yanchang Han^*, Yongsheng Han, Ji Li, Chaoqiang Tan

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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

Abstract

The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in L²space and the theory of nonhomogeneous singular integral operators as pivotal components.

Original language	English
Pages (from-to)	299-370
Number of pages	72
Journal	Analysis in Theory and Applications
Volume	41
Issue number	4
DOIs	https://doi.org/10.4208/ata.2025.deng90.01
Publication status	Published - 2025

Keywords

local Dunkl-Hardy space
Nonhomogeneous Dunkl-Calder ón-Zygmund singular integral
weak local wavelet decomposition

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10.4208/ata.2025.deng90.01

Cite this

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title = "Singular integral and local Hardy spaces in Dunkl setting",

abstract = "The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in L2 space and the theory of nonhomogeneous singular integral operators as pivotal components.",

keywords = "local Dunkl-Hardy space, Nonhomogeneous Dunkl-Calder {\'o}n-Zygmund singular integral, weak local wavelet decomposition",

author = "Yanchang Han and Yongsheng Han and Ji Li and Chaoqiang Tan",

year = "2025",

doi = "10.4208/ata.2025.deng90.01",

language = "English",

volume = "41",

pages = "299--370",

journal = "Analysis in Theory and Applications",

issn = "1672-4070",

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TY - JOUR

T1 - Singular integral and local Hardy spaces in Dunkl setting

AU - Han, Yanchang

AU - Han, Yongsheng

AU - Li, Ji

AU - Tan, Chaoqiang

PY - 2025

Y1 - 2025

N2 - The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in L2 space and the theory of nonhomogeneous singular integral operators as pivotal components.

AB - The objective of this paper is to establish the local Hardy space in the Dunkl setting, which pertains to the geometric framework defined by both the Euclidean metric and the Dunkl metric, the latter being influenced by finite reflection groups. This study leverages the weak local wavelet decomposition in L2 space and the theory of nonhomogeneous singular integral operators as pivotal components.

KW - local Dunkl-Hardy space

KW - Nonhomogeneous Dunkl-Calder ón-Zygmund singular integral

KW - weak local wavelet decomposition

UR - https://www.scopus.com/pages/publications/105032437182

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

U2 - 10.4208/ata.2025.deng90.01

DO - 10.4208/ata.2025.deng90.01

M3 - Article

AN - SCOPUS:105032437182

SN - 1672-4070

VL - 41

SP - 299

EP - 370

JO - Analysis in Theory and Applications

JF - Analysis in Theory and Applications

IS - 4

ER -

Singular integral and local Hardy spaces in Dunkl setting

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DP22: Harmonic analysis of Laplacians in curved spaces

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Singular integral and local Hardy spaces in Dunkl setting

Abstract

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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