Schr?dinger-type propagators, pseudodifferential operators and modulation spaces

摘要

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 non-degenerate generalized quadratic forms that includes Schr?dinger propagators and pseudodifferential operators. As a byproduct, we obtain a characterization of all exponents p, q, r1, r2, t1, t2 ∈ [1,∞] of modulation spaces such that a symbol in M~(p,q)(?~(2d)) gives a pseudodifferential operator that is continuous from M~(r1,r2) (?~d) into M~(t1,t2) (?~d).