Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces

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 wellknown results in the literature. For example we generalize the classical result by Cordero and Nicola that if 1 + p 1 ql 1 p1 1 + p2 , 1 + p 1 ql 1 q1 1 + q2 , pj, qj qql, q 5 p and a is an element of Mp,q, then the pseudo-differential operator Op(a) is continuous from Mp1,q1 to Mp2,q2. We also show that the entropy functional E phi possess suitable continuity properties on a suitable Orlicz modulation space M phi satisfying Mp subset of M phi subset of M2, though E phi is discontinuous on M2 = L2.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

Automated summary

This article deduces continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces, extending well-known results in the literature. The article also shows the continuity properties of the entropy functional on a suitable Orlicz modulation space, even though it is discontinuous on M2 = L2.