Schrödinger-type propagators, pseudodifferential operators and modulation spaces (Q2854245)

Several continuity results for Fourier integral operators acting between modulation spaces are proved. It is assume that a phase function of the operator is tame and that its symbol belongs to a modulation space. The assumption concerning the phase function cover pseudo-differential operators in Kohn-Nirenberg form and generalized metaplectic operators. A few continuity results are proved. The most interesting one gives sufficient and necessary conditions for continuity of the pseudo-differential operators with symbol in a modulation space acting between modulation spaces or between closures of Schwartz functions in the modulation spaces. Some consequences concerning the boundedness of the Fourier integral operators in Wiener amalgam spaces are also proved.