Trace ideals for Fourier integral operators with non-smooth symbols II

TL;DR

This paper studies Fourier integral operators with non-smooth symbols and phase functions, establishing their continuity and Schatten-von Neumann properties on modulation spaces, extending understanding of their boundedness in non-ideal conditions.

Contribution

It introduces new conditions on symbols and phase functions in modulation spaces, proving continuity and Schatten-von Neumann properties for these operators.

Findings

Operators are continuous on modulation spaces.

Operators exhibit Schatten-von Neumann properties.

Results extend previous work to non-smooth symbols and phases.

Abstract

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann properties of such operators when acting on modulation spaces.