Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type

TL;DR

This paper investigates trace properties of modulation spaces of Gelfand-Shilov distributions and applies these findings to establish equivalences between different classes of pseudo-differential operators with amplitudes in modulation spaces.

Contribution

It introduces new trace properties for modulation spaces of Gelfand-Shilov distributions and connects pseudo-differential operators of amplitude type to those of normal type within these spaces.

Findings

Established trace properties for modulation spaces of Gelfand-Shilov distributions.

Proved equivalence of pseudo-differential operators with amplitudes and symbols in modulation spaces.

Extended the understanding of operator classes in the context of modulation spaces.

Abstract

We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of normal type whose symbols belong to (other) modulation spaces.