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

Abstract

We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand–Shilov distributions.We use these results to show that [Formula: see text]dos with amplitudes in suitable modulation spaces, agree with normal type [Formula: see text]dos whose symbols belong to (other) modulation spaces. In particular we extend earlier trace results for modulation spaces, to include quasi-Banach modulation spaces. We also apply our results to extend earlier results on Schatten-von Neumann and nuclear properties for [Formula: see text]dos with amplitudes in modulation spaces.