Schatten classes and commutator in the two weight setting, I. Hilbert transform

Michael Lacey; Ji Li; Brett D. Wick

doi:10.1007/s11118-023-10072-x

Schatten classes and commutator in the two weight setting, I. Hilbert transform

Michael Lacey, Ji Li^*, Brett D. Wick

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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

2 Citations (Scopus)

15 Downloads (Pure)

Abstract

We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class S_p result for dyadic paraproducts, where 1 < p < ∞. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

Original language	English
Pages (from-to)	875-894
Number of pages	20
Journal	Potential Analysis
Volume	60
Issue number	2
Early online date	6 Apr 2023
DOIs	https://doi.org/10.1007/s11118-023-10072-x
Publication status	Published - Feb 2024

Bibliographical note

Keywords

Commutator
Dyadic structure
Hilbert transform
Schatten class
Weighted Besov space

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10.1007/s11118-023-10072-xLicence: CC BY

Publisher version (open access)Final published version, 881 KBLicence: CC BY

Cite this

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N2 - We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class Sp result for dyadic paraproducts, where 1 < p < ∞. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

AB - We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class Sp result for dyadic paraproducts, where 1 < p < ∞. We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

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KW - Dyadic structure

KW - Hilbert transform

KW - Schatten class

KW - Weighted Besov space

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Schatten classes and commutator in the two weight setting, I. Hilbert transform

Abstract

Bibliographical note

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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Schatten classes and commutator in the two weight setting, I. Hilbert transform

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

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DP22: Harmonic analysis of Laplacians in curved spaces

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