Schrödinger-type propagators, pseudodifferential operators and modulation spaces

We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents p, q, r 1 , r 2 , t 1 , t 2 ∈ [1, ∞] of modulation spaces such that a symbol in M p,q (R 2d) gives a pseudodifferen-tial operator that is continuous from M r1,r2 (R d) into M t1,t2 (R d).