The Riesz transform and fractional integral operators in the Bessel setting

Jorge J. Betancor; Xuan Thinh Duong; Ming-Yi Lee; Ji Li; Brett D. Wick

doi:10.1007/s00020-025-02801-1

The Riesz transform and fractional integral operators in the Bessel setting

Jorge J. Betancor, Xuan Thinh Duong, Ming-Yi Lee, Ji Li, Brett D. Wick

School of Mathematical and Physical Sciences

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

6 Citations (Scopus)

Abstract

Fix λ>0. Consider the Bessel operator Δ_λ:= - d²/d^x2- 2^λ/x d/dx on R₊, where R₊ := (0,∞) and dm_λ := x^2λdx with dx the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel–Lizorkin spaces associated with Δ_λ. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.

Original language	English
Article number	15
Pages (from-to)	1-29
Number of pages	29
Journal	Integral Equations and Operator Theory
Volume	97
Issue number	2
DOIs	https://doi.org/10.1007/s00020-025-02801-1
Publication status	Published - 5 Jun 2025

Keywords

Bessel operator
Bessel Riesz transform
commutator

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10.1007/s00020-025-02801-1

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abstract = "Fix λ>0. Consider the Bessel operator Δλ:= - d2/dx2 - 2λ/x d/dx on R+, where R+ := (0,∞) and dmλ := x2λdx with dx the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel–Lizorkin spaces associated with Δλ. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.",

keywords = "Bessel operator, Bessel Riesz transform, commutator",

author = "Betancor, \{Jorge J.\} and Duong, \{Xuan Thinh\} and Ming-Yi Lee and Ji Li and Wick, \{Brett D.\}",

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doi = "10.1007/s00020-025-02801-1",

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T1 - The Riesz transform and fractional integral operators in the Bessel setting

AU - Betancor, Jorge J.

AU - Duong, Xuan Thinh

AU - Lee, Ming-Yi

AU - Li, Ji

AU - Wick, Brett D.

PY - 2025/6/5

Y1 - 2025/6/5

N2 - Fix λ>0. Consider the Bessel operator Δλ:= - d2/dx2 - 2λ/x d/dx on R+, where R+ := (0,∞) and dmλ := x2λdx with dx the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel–Lizorkin spaces associated with Δλ. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.

AB - Fix λ>0. Consider the Bessel operator Δλ:= - d2/dx2 - 2λ/x d/dx on R+, where R+ := (0,∞) and dmλ := x2λdx with dx the Lebesgue measure. We provide a deeper study of the Bessel Riesz transform and fractional integral operator via the related Besov and Triebel–Lizorkin spaces associated with Δλ. Moreover, we investigate some possible characterization of the commutator of fractional integral operator, which was missing in the literature of the Bessel setting.

KW - Bessel operator

KW - Bessel Riesz transform

KW - commutator

UR - https://www.scopus.com/pages/publications/105007720135

U2 - 10.1007/s00020-025-02801-1

DO - 10.1007/s00020-025-02801-1

M3 - Article

AN - SCOPUS:105007720135

SN - 0378-620X

VL - 97

SP - 1

EP - 29

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

M1 - 15

ER -

The Riesz transform and fractional integral operators in the Bessel setting

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Keywords

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