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

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.

33 pages. This second version contains 10 more pages compared to the first version. Some results are improved and some other results are added, especially on pseudo-differential operators