Pseudodifferential Operators on Lp, Wiener Amalgam and Modulation Spaces”

We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces M^p, q, acting on a given Lebesgue space L^r. Namely, we find the full range of triples (p, q, r), for which such a boundedness occurs. More generally, we completely characterize the same problem for operators acting on Wiener amalgam space W(L^r, L^s) and even on modulation spaces M^r, s. Finally, the action of pseudodifferential operators with symbols in $W(\mathcal FL^1,L^{\infty})$ is also investigated.