Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

Xudong Lai; Xiao Xiong; Yue Zhang

doi:10.1007/s00209-026-04067-8

Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

Xudong Lai
, Xiao Xiong
, Yue Zhang^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

Abstract

For 1<p<∞, we establish the Lp boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori Lp(Tθd), and quantum Euclidean space Lp(Rθd). In particular, the norm constants in both cases are independent of the dimension d when 2≤p<∞.

Original language	English
Article number	59
Journal	Mathematische Zeitschrift
Volume	313
Issue number	3
DOIs	https://doi.org/10.1007/s00209-026-04067-8
State	Published - Jul 2026

Keywords

Dimension-free
Maximal Riesz transform
Quantum Euclidean space
Quantum tori
Transference principle

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abstract = "For 1",

keywords = "Dimension-free, Maximal Riesz transform, Quantum Euclidean space, Quantum tori, Transference principle",

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AU - Xiong, Xiao

AU - Zhang, Yue

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2026.

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Y1 - 2026/7

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KW - Dimension-free

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KW - Quantum tori

KW - Transference principle

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VL - 313

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Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

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Keywords

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