2024/09/09 by Aparajita Dasgupta, Dasgupta, Aparajita, Anirudha Poria +1
Mathematics · #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2409.05373
In this paper, we introduce Orlicz spaces on \mathbb Zn × \mathbb Tn and Orlicz modulation spaces on \mathbb Zn, and present some basic properties such as inclusion relations, convolution relations, and duality of these spaces. We show that the Orlicz modulation space MΦ(\mathbb Zn) is close to the modulation space M2(\mathbb Zn) for some particular Young function Φ. Then, we study a class of pseudo-differential operators known as time-frequency localization operators on \mathbb Zn, which depend on a symbol ς and two windows functions g1 and g2. Using appropriate classes for symbols, we study the boundedness of the localization operators on Orlicz modulation spaces on \mathbb Zn. Also, we show that these operators are compact and in the Schatten--von Neumann classes.