Hardy spaces associated to generalized Hardy operators and applications

The Anh Bui; Georges Nader

doi:10.1007/s00030-022-00765-4

Hardy spaces associated to generalized Hardy operators and applications

The Anh Bui^*, Georges Nader

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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

6 Citations (Scopus)

48 Downloads (Pure)

Abstract

In this paper, we will study the Hardy and BMO spaces associated to the generalized Hardy operator L_α= (- Δ) ^α^/²+ a| x| ^-^α. Similarly to the classical Hardy and BMO spaces, we will prove that our new function spaces will enjoy some important results such as molecular decomposition and duality. As applications, we show the boundedness of the spectral multiplier of Laplace transform type and the Sobolev norm inequalities involving the generalized Hardy operator.

Original language	English
Article number	40
Pages (from-to)	1-40
Number of pages	40
Journal	Nonlinear Differential Equations and Applications
Volume	29
Issue number	4
DOIs	https://doi.org/10.1007/s00030-022-00765-4
Publication status	Published - Jul 2022

Bibliographical note

Copyright © 2022, The Author(s). 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.

Keywords

BMO space
Generalized Hardy operator
Hardy space
Heat kernel

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10.1007/s00030-022-00765-4Licence: CC BY

Publisher version (open access)Final published version, 636 KBLicence: CC BY

Cite this

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abstract = "In this paper, we will study the Hardy and BMO spaces associated to the generalized Hardy operator Lα= (- Δ) α/2+ a| x| -α. Similarly to the classical Hardy and BMO spaces, we will prove that our new function spaces will enjoy some important results such as molecular decomposition and duality. As applications, we show the boundedness of the spectral multiplier of Laplace transform type and the Sobolev norm inequalities involving the generalized Hardy operator.",

keywords = "BMO space, Generalized Hardy operator, Hardy space, Heat kernel",

author = "Bui, {The Anh} and Georges Nader",

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AU - Bui, The Anh

AU - Nader, Georges

N1 - Copyright © 2022, The Author(s). 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 - 2022/7

Y1 - 2022/7

N2 - In this paper, we will study the Hardy and BMO spaces associated to the generalized Hardy operator Lα= (- Δ) α/2+ a| x| -α. Similarly to the classical Hardy and BMO spaces, we will prove that our new function spaces will enjoy some important results such as molecular decomposition and duality. As applications, we show the boundedness of the spectral multiplier of Laplace transform type and the Sobolev norm inequalities involving the generalized Hardy operator.

AB - In this paper, we will study the Hardy and BMO spaces associated to the generalized Hardy operator Lα= (- Δ) α/2+ a| x| -α. Similarly to the classical Hardy and BMO spaces, we will prove that our new function spaces will enjoy some important results such as molecular decomposition and duality. As applications, we show the boundedness of the spectral multiplier of Laplace transform type and the Sobolev norm inequalities involving the generalized Hardy operator.

KW - BMO space

KW - Generalized Hardy operator

KW - Hardy space

KW - Heat kernel

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UR - http://purl.org/au-research/grants/arc/DP220100285

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DO - 10.1007/s00030-022-00765-4

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VL - 29

SP - 1

EP - 40

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 4

M1 - 40

ER -

Hardy spaces associated to generalized Hardy operators and applications

Abstract

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Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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Hardy spaces associated to generalized Hardy operators and applications

Abstract

Bibliographical note

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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