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

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

1 Scopus citations

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+∑j=1dR˜_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
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	262
DOIs	https://doi.org/10.1016/j.na.2025.113916
State	Published - Jan 2026

Keywords

CMO(ℝ, dω)
Dunkl operator
Dunkl–Riesz transform
H(ℝ, dω)

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10.1016/j.na.2025.113916

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title = "Fefferman{\textendash}Stein type decomposition of CMO spaces in the Dunkl setting and an application",

abstract = "In this paper, we establish the Fefferman{\textendash}Stein type decomposition of the CMO space in the Dunkl setting. That is f∈CMO(Rd,dω) if and only if f=f0+∑j=1dR˜jfj,where f0,f1,…,fd∈C0(Rd) and R˜j, j=0,1,…,d, represent the Dunkl{\textendash}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(ℝ, dω), Dunkl operator, Dunkl{\textendash}Riesz transform, H(ℝ, dω)",

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

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",

year = "2026",

month = jan,

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

language = "English",

volume = "262",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

}

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+∑j=1dR˜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+∑j=1dR˜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(ℝ, dω)

KW - Dunkl operator

KW - Dunkl–Riesz transform

KW - H(ℝ, dω)

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

U2 - 10.1016/j.na.2025.113916

DO - 10.1016/j.na.2025.113916

M3 - Article

AN - SCOPUS:105013386275

SN - 0362-546X

VL - 262

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

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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