English

Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces

Functional Analysis 2023-10-27 v2

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 MpM^p and M2M^2 when p<2p<2, though the functional is discontinuous on M2=L2M^2=L^2.

Keywords

Cite

@article{arxiv.2304.09558,
  title  = {Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces},
  author = {Anupam Gumber and Nimit Rana and Joachim Toft and Rüya Üster},
  journal= {arXiv preprint arXiv:2304.09558},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-28T10:10:50.940Z