Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application

Qingdong Guo; Ji Li; Brett D. Wick

doi:10.1016/j.na.2025.113916

Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application

Qingdong Guo, Ji Li, Brett D. Wick

School of Mathematical and Physical Sciences

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

Abstract

In this paper, we establish the Fefferman–Stein type decomposition of the CMO space in the Dunkl setting. That is f∈CMO(ℝ^d,dω) if and only if f=f₀+ ∑^d_j=1R˜_jf_j, where f₀,f₁,…,f_d∈C₀(ℝ^d) and R˜_j, j=0,1,…,d, represent the Dunkl–Riesz transforms. Our main tool is to characterize CMO(ℝ^d,dω) via two approximations, which are new even for the classical space CMO(ℝ^d). As a direct application of our characterization of CMO(ℝ^d,dω), we prove the duality of CMO(ℝ^d,dω) with H¹(ℝ^d,dω).

Original language	English
Article number	113916
Pages (from-to)	1-27
Number of pages	27
Journal	Nonlinear Analysis
Volume	262
DOIs	https://doi.org/10.1016/j.na.2025.113916
Publication status	Published - Jan 2026

Keywords

CMO(ℝd, dω)
Dunkl operator
Dunkl–Riesz transform
H1(ℝd, dω)

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10.1016/j.na.2025.113916

Cite this

@article{38986b94de064b408cdbc1798d35ea55,

title = "Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application",

abstract = "In this paper, we establish the Fefferman–Stein type decomposition of the CMO space in the Dunkl setting. That is f∈CMO(ℝd,dω) if and only if f=f0 + ∑dj=1R˜jfj, where f0,f1,…,fd ∈C0(ℝd) and R˜j, j=0,1,…,d, represent the Dunkl–Riesz transforms. Our main tool is to characterize CMO(ℝd,dω) via two approximations, which are new even for the classical space CMO(ℝd). As a direct application of our characterization of CMO(ℝd,dω), we prove the duality of CMO(ℝd,dω) with H1(ℝd,dω).",

keywords = "CMO(ℝd, dω), Dunkl operator, Dunkl–Riesz transform, H1(ℝd, dω)",

author = "Qingdong Guo and Ji Li and Wick, \{Brett D.\}",

year = "2026",

month = jan,

doi = "10.1016/j.na.2025.113916",

language = "English",

volume = "262",

pages = "1--27",

journal = "Nonlinear Analysis",

issn = "0362-546X",

publisher = "Elsevier",

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TY - JOUR

T1 - Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application

AU - Guo, Qingdong

AU - Li, Ji

AU - Wick, Brett D.

PY - 2026/1

Y1 - 2026/1

N2 - In this paper, we establish the Fefferman–Stein type decomposition of the CMO space in the Dunkl setting. That is f∈CMO(ℝd,dω) if and only if f=f0 + ∑dj=1R˜jfj, where f0,f1,…,fd ∈C0(ℝd) and R˜j, j=0,1,…,d, represent the Dunkl–Riesz transforms. Our main tool is to characterize CMO(ℝd,dω) via two approximations, which are new even for the classical space CMO(ℝd). As a direct application of our characterization of CMO(ℝd,dω), we prove the duality of CMO(ℝd,dω) with H1(ℝd,dω).

AB - In this paper, we establish the Fefferman–Stein type decomposition of the CMO space in the Dunkl setting. That is f∈CMO(ℝd,dω) if and only if f=f0 + ∑dj=1R˜jfj, where f0,f1,…,fd ∈C0(ℝd) and R˜j, j=0,1,…,d, represent the Dunkl–Riesz transforms. Our main tool is to characterize CMO(ℝd,dω) via two approximations, which are new even for the classical space CMO(ℝd). As a direct application of our characterization of CMO(ℝd,dω), we prove the duality of CMO(ℝd,dω) with H1(ℝd,dω).

KW - CMO(ℝd, dω)

KW - Dunkl operator

KW - Dunkl–Riesz transform

KW - H1(ℝd, dω)

UR - https://www.scopus.com/pages/publications/105013386275

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

U2 - 10.1016/j.na.2025.113916

DO - 10.1016/j.na.2025.113916

M3 - Article

SN - 0362-546X

VL - 262

SP - 1

EP - 27

JO - Nonlinear Analysis

JF - Nonlinear Analysis

M1 - 113916

ER -

Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application

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Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application

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DP22: Harmonic analysis of Laplacians in curved spaces

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