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arXiv · 2409.05373

Localization operators on discrete Orlicz modulation spaces

Aparajita Dasgupta·Anirudha Poria
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Abstract

In this paper, 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.

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Aparajita Dasgupta, Anirudha Poria. 2024-09-09. Localization operators on discrete Orlicz modulation spaces. https://doi.org/10.4153/s0008439525101458

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