Localization operators on discrete Orlicz modulation spaces

In this paper, we introduce Orlicz spaces on Zn ×Tn and Orlicz modulation spaces on Zn, and study inclusion relations, convolution relations, and duality of these spaces. We show that the Orlicz modulation space Mκ(Zn) is close to the modulation space M2(Zn) for some particular Young function κ. Then, we study localization operators on Zn. In particular, using appropriate classes for symbols, we prove that these operators are bounded on Orlicz modulation spaces on Zn, compact and in the Schatten von Neumann classes.