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 psi dos with amplitudes in suitable modulation spaces, agree with normal type psi 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 psi dos with amplitudes in modulation spaces.