Abstract
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 is also investigated.
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