Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

The Anh Bui; Xuan Thinh Duong

doi:10.1007/s00365-019-09493-y

Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

The Anh Bui, Xuan Thinh Duong^*

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

Consider the Hermite operator H=−Δ+|x|² on the Euclidean space Rⁿ. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.

Original language	English
Pages (from-to)	85-120
Number of pages	36
Journal	Constructive Approximation
Volume	53
Issue number	1
Early online date	8 Jan 2020
DOIs	https://doi.org/10.1007/s00365-019-09493-y
Publication status	Published - Feb 2021

Keywords

Hermite operator
Higher order Riesz transforms
Besov space
Triebel–Lizorkin space

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10.1007/s00365-019-09493-y

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title = "Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces",

abstract = "Consider the Hermite operator H=−Δ+|x|2 on the Euclidean space Rn. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.",

keywords = "Hermite operator, Higher order Riesz transforms, Besov space, Triebel–Lizorkin space",

author = "Bui, \{The Anh\} and Duong, \{Xuan Thinh\}",

year = "2021",

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doi = "10.1007/s00365-019-09493-y",

language = "English",

volume = "53",

pages = "85--120",

journal = "Constructive Approximation",

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T1 - Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

AU - Bui, The Anh

AU - Duong, Xuan Thinh

PY - 2021/2

Y1 - 2021/2

N2 - Consider the Hermite operator H=−Δ+|x|2 on the Euclidean space Rn. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.

AB - Consider the Hermite operator H=−Δ+|x|2 on the Euclidean space Rn. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.

KW - Hermite operator

KW - Higher order Riesz transforms

KW - Besov space

KW - Triebel–Lizorkin space

UR - https://www.scopus.com/pages/publications/85077527858

UR - http://purl.org/au-research/grants/arc/DP190100970

U2 - 10.1007/s00365-019-09493-y

DO - 10.1007/s00365-019-09493-y

M3 - Article

AN - SCOPUS:85077527858

SN - 0176-4276

VL - 53

SP - 85

EP - 120

JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -

Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

Abstract

Keywords

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Harmonic analysis: function spaces and partial differential equations

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Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

Abstract

Keywords

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Other files and links

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Projects

Harmonic analysis: function spaces and partial differential equations

Cite this