Fourier integral operators on Orlicz modulation spaces

TL;DR

This paper studies the behavior of Fourier integral operators with amplitudes in Orlicz modulation spaces, focusing on their continuity and Schatten-von Neumann properties on these spaces.

Contribution

It introduces new results on the boundedness and Schatten class properties of Fourier integral operators with non-smooth phase functions in Orlicz modulation spaces.

Findings

Fourier integral operators are continuous on Orlicz modulation spaces.

Operators exhibit Schatten-von Neumann properties under certain conditions.

Phase functions with second order derivatives in modulation spaces are considered.

Abstract

We establish continuity and Schatten-von Neumann properties for Fourier integral operators with amplitudes in Orlicz modulation spaces, when acting on other Orlicz modulation spaces themselves. The phase functions are non smooth and admit second order derivatives in suitable classes of modulation spaces.