Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative

Z. Gong; J. Li; B. D. Wick

doi:10.1007/s10476-023-0246-y

Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative

Z. Gong
, J. Li
, B. D. Wick

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L ² spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.

Original language	English
Pages (from-to)	971-1006
Number of pages	36
Journal	Analysis Mathematica
Volume	49
Issue number	4
DOIs	https://doi.org/10.1007/s10476-023-0246-y
State	Published - Dec 2023

Keywords

Besov space
commutator
Riesz transform
Schatten class

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10.1007/s10476-023-0246-y

Cite this

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abstract = "In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L 2 spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.",

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AU - Gong, Z.

AU - Li, J.

AU - Wick, B. D.

PY - 2023/12

Y1 - 2023/12

N2 - In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L 2 spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.

AB - In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L 2 spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.

KW - Besov space

KW - commutator

KW - Riesz transform

KW - Schatten class

UR - https://www.scopus.com/pages/publications/85176461514

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DO - 10.1007/s10476-023-0246-y

M3 - Article

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SN - 0133-3852

VL - 49

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EP - 1006

JO - Analysis Mathematica

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IS - 4

ER -

Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative

Abstract

Keywords

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