Compactness of Riesz transform commutator associated with Bessel operators

Xuan Thinh Duong; Ji Li; Suzhen Mao; Huoxiong Wu; Dongyong Yang

doi:10.1007/s11854-018-0048-5

Compactness of Riesz transform commutator associated with Bessel operators

Xuan Thinh Duong, Ji Li, Suzhen Mao, Huoxiong Wu, Dongyong Yang^*

^*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R₊:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R₊, x^2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R⁺, x^2λdx) is in CMO(R⁺, x^2λdx) if and only if the Riesz transform commutator xxxx is compact on L^p(R⁺, x^2λdx) for all p ∈ (1,∞).

Original language	English
Pages (from-to)	639-673
Number of pages	35
Journal	Journal d'Analyse Mathematique
Volume	135
Issue number	2
DOIs	https://doi.org/10.1007/s11854-018-0048-5
Publication status	Published - 1 Jun 2018

Access to Document

10.1007/s11854-018-0048-5

Cite this

@article{d22904d5976d422caac3cef7b49beef3,

title = "Compactness of Riesz transform commutator associated with Bessel operators",

abstract = "Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fr{\'e}chet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).",

author = "Duong, \{Xuan Thinh\} and Ji Li and Suzhen Mao and Huoxiong Wu and Dongyong Yang",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s11854-018-0048-5",

language = "English",

volume = "135",

pages = "639--673",

journal = "Journal d'Analyse Mathematique",

issn = "0021-7670",

publisher = "Springer, Springer Nature",

number = "2",

}

TY - JOUR

T1 - Compactness of Riesz transform commutator associated with Bessel operators

AU - Duong, Xuan Thinh

AU - Li, Ji

AU - Mao, Suzhen

AU - Wu, Huoxiong

AU - Yang, Dongyong

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).

AB - Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).

UR - https://www.scopus.com/pages/publications/85050149699

UR - http://purl.org/au-research/grants/arc/DP140100649

UR - http://purl.org/au-research/grants/arc/DP160100153

U2 - 10.1007/s11854-018-0048-5

DO - 10.1007/s11854-018-0048-5

M3 - Article

AN - SCOPUS:85050149699

SN - 0021-7670

VL - 135

SP - 639

EP - 673

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

IS - 2

ER -

Compactness of Riesz transform commutator associated with Bessel operators

Abstract

Access to Document

Other files and links

Fingerprint

Cite this