Schatten classes and commutators of Riesz transform on Heisenberg group and applications

Zhijie Fan; Michael Lacey; Ji Li

doi:10.1007/s00041-023-09995-1

Schatten classes and commutators of Riesz transform on Heisenberg group and applications

Zhijie Fan, Michael Lacey, Ji Li

School of Mathematical and Physical Sciences

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

8 Citations (Scopus)

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Abstract

We study commutators with the Riesz transforms on the Heisenberg group Hⁿ. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms on Hⁿ among other settings.

Original language	English
Article number	17
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Fourier Analysis and Applications
Volume	29
Issue number	2
DOIs	https://doi.org/10.1007/s00041-023-09995-1
Publication status	Published - Apr 2023

Bibliographical note

Keywords

Schatten class
Commutator
Riesz transform
Heisenberg group
Besov space

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10.1007/s00041-023-09995-1Licence: CC BY

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

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abstract = "We study commutators with the Riesz transforms on the Heisenberg group Hn. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szeg{\H o} projection and second order Riesz transforms on Hn among other settings.",

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AU - Lacey, Michael

AU - Li, Ji

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N2 - We study commutators with the Riesz transforms on the Heisenberg group Hn. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms on Hn among other settings.

AB - We study commutators with the Riesz transforms on the Heisenberg group Hn. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms on Hn among other settings.

KW - Schatten class

KW - Commutator

KW - Riesz transform

KW - Heisenberg group

KW - Besov space

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DO - 10.1007/s00041-023-09995-1

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JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 2

M1 - 17

ER -

Schatten classes and commutators of Riesz transform on Heisenberg group and applications

Abstract

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Keywords

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