Besov and Triebel-Lizorkin spaces associated to Hermite operators

The Anh Bui; Xuan Thinh Duong

doi:10.1007/s00041-014-9378-6

Besov and Triebel-Lizorkin spaces associated to Hermite operators

The Anh Bui^*, Xuan Thinh Duong

^*Corresponding author for this work

Research output: Contribution to journal › Article

14 Citations (Scopus)

Abstract

Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.

Original language	English
Pages (from-to)	405-448
Number of pages	44
Journal	Journal of Fourier Analysis and Applications
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s00041-014-9378-6
Publication status	Published - Apr 2015

Keywords

Besov space
Hermite operator
Molecular decomposition
Triebel–Lizorkin space

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10.1007/s00041-014-9378-6

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abstract = "Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.",

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T1 - Besov and Triebel-Lizorkin spaces associated to Hermite operators

AU - Bui, The Anh

AU - Duong, Xuan Thinh

PY - 2015/4

Y1 - 2015/4

N2 - Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.

AB - Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.

KW - Besov space

KW - Hermite operator

KW - Molecular decomposition

KW - Triebel–Lizorkin space

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EP - 448

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

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