Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces

Abstract

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. We also show that the entropy functional is continuous on a suitable Orlicz modulation space between $M^p$ and $M^2$ when $p<2$, though the functional is discontinuous on $M^2=L^2$.

A proof of a statement in the first version is added. Because of this, the number of pages has increased by 6 to totally 34 pages. It has also changed the structure compared to the first version. Because of this, the title and abstract are changed