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Localization operators on discrete Orlicz modulation spaces

Part of: Integral, integro-differential, and pseudodifferential operators Special classes of linear operators Harmonic analysis in several variables

Published online by Cambridge University Press:  14 November 2025

Aparajita Dasgupta Open the ORCID record for Aparajita Dasgupta [Opens in a new window]  and
Anirudha Poria Open the ORCID record for Anirudha Poria [Opens in a new window]
Aparajita Dasgupta
Affiliation:
Indian Institute of Technology, Delhi , India e-mail: adasgupta@maths.iitd.ac.in
Anirudha Poria*
Affiliation:
Xi’an Jiaotong–Liverpool University , China
*
e-mail: Anirudha.Poria@xjtlu.edu.cn
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Abstract

In this article, we introduce Orlicz spaces on $ \mathbb Z^n \times \mathbb T^n $ and Orlicz modulation spaces on $\mathbb Z^n$, and study inclusion relations, convolution relations, and duality of these spaces. We show that the Orlicz modulation space $M^{\Phi }(\mathbb Z^n)$ is close to the modulation space $M^{2}(\mathbb Z^n)$ for some particular Young function $\Phi $. Then, we study localization operators on $\mathbb Z^n$. In particular, using appropriate classes for symbols, we prove that these operators are bounded on Orlicz modulation spaces on $\mathbb Z^n$, compact and in the Schatten–von Neumann classes.

Keywords

Localization operatorsdiscrete Orlicz modulation spacesYoung functionscompact operatorsSchatten–von Neumann class

MSC classification

Primary: 47G30: Pseudodifferential operators
Secondary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) 42B35: Function spaces arising in harmonic analysis

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 21
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The second author is partially supported by the XJTLU Research Development Fund (RDF-23-01-027).

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