Calderón–Zygmund operators and endpoint spaces for Hermite expansions

The Anh Bui; Fu Ken Ly

doi:10.1007/s00041-024-10130-x

Calderón–Zygmund operators and endpoint spaces for Hermite expansions

The Anh Bui, Fu Ken Ly^*

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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

3 Citations (Scopus)

13 Downloads (Pure)

Abstract

Let L=-Δ+|x|² be the Hermite operator on Rⁿ, and T be a Calderon–Zygmund type operator that is modelled on certain singular integrals related to L. We establish necessary and sufficient conditions for T to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to L. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to L.

Original language	English
Article number	75
Pages (from-to)	1-57
Number of pages	57
Journal	Journal of Fourier Analysis and Applications
Volume	30
Issue number	6
DOIs	https://doi.org/10.1007/s00041-024-10130-x
Publication status	Published - Dec 2024

Bibliographical note

Keywords

Hermite operators
Hardy spaces
Molecules
Pseudodifferential operators
Riesz transforms

Access to Document

10.1007/s00041-024-10130-xLicence: CC BY

Publisher version (open access)Final published version, 1.09 MBLicence: CC BY

Cite this

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title = "Calder{\'o}n–Zygmund operators and endpoint spaces for Hermite expansions",

abstract = "Let L=-Δ+|x|2 be the Hermite operator on Rn, and T be a Calderon–Zygmund type operator that is modelled on certain singular integrals related to L. We establish necessary and sufficient conditions for T to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to L. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to L.",

keywords = "Hermite operators, Hardy spaces, Molecules, Pseudodifferential operators, Riesz transforms",

author = "Bui, \{The Anh\} and Ly, \{Fu Ken\}",

note = "{\textcopyright} The Author(s) 2024. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2024",

month = dec,

doi = "10.1007/s00041-024-10130-x",

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TY - JOUR

T1 - Calderón–Zygmund operators and endpoint spaces for Hermite expansions

AU - Bui, The Anh

AU - Ly, Fu Ken

N1 - © The Author(s) 2024. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2024/12

Y1 - 2024/12

N2 - Let L=-Δ+|x|2 be the Hermite operator on Rn, and T be a Calderon–Zygmund type operator that is modelled on certain singular integrals related to L. We establish necessary and sufficient conditions for T to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to L. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to L.

AB - Let L=-Δ+|x|2 be the Hermite operator on Rn, and T be a Calderon–Zygmund type operator that is modelled on certain singular integrals related to L. We establish necessary and sufficient conditions for T to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to L. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to L.

KW - Hermite operators

KW - Hardy spaces

KW - Molecules

KW - Pseudodifferential operators

KW - Riesz transforms

UR - https://www.scopus.com/pages/publications/85211119390

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

U2 - 10.1007/s00041-024-10130-x

DO - 10.1007/s00041-024-10130-x

M3 - Article

AN - SCOPUS:85211119390

SN - 1069-5869

VL - 30

SP - 1

EP - 57

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 6

M1 - 75

ER -

Calderón–Zygmund operators and endpoint spaces for Hermite expansions

Abstract

Bibliographical note

Keywords

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Harmonic Analysis and Partial Differential Operators

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Calderón–Zygmund operators and endpoint spaces for Hermite expansions

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

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Harmonic Analysis and Partial Differential Operators

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