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

^*Corresponding author for this work

School of Mathematical and Physical Sciences

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

Abstract

In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L² 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
Publication status	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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title = "Besov spaces, Schatten classes and weighted versions of the quantised derivative",

abstract = "In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted L2 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.",

keywords = "Besov space, commutator, Riesz transform, Schatten class",

author = "Z. Gong and J. Li and Wick, {B. D.}",

year = "2023",

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T1 - Besov spaces, Schatten classes and weighted versions of the quantised derivative

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 L2 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 L2 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

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

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DO - 10.1007/s10476-023-0246-y

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JF - Analysis Mathematica

IS - 4

ER -

Besov spaces, Schatten classes and weighted versions of the quantised derivative

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Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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Besov spaces, Schatten classes and weighted versions of the quantised derivative

Abstract

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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