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(F L^1,L^\infty) is also investigated.
Pseudodifferential operators on L^p, Wiener amalgam and modulation spaces
CORDERO, Elena;
2010-01-01
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 W(F L^1,L^\infty) is also investigated.
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