Archivio Istituzionale della RicercaWe 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¨odinger 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 Mp,q(R2d) gives a pseudodifferential operator that is continuous from Mr1,r2 (Rd) into Mt1,t2 (Rd).
Schrodinger-type propagators, pseudodifferential operators and modulation spaces / Elena, Cordero; Tabacco, Anita Maria; Patrik, Wahlberg. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - ELETTRONICO. - (2013), pp. 375-395. [10.1112/jlms/jdt020]
Schrodinger-type propagators, pseudodifferential operators and modulation spaces
TABACCO, Anita Maria;
2013
Abstract
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¨odinger 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 Mp,q(R2d) gives a pseudodifferential operator that is continuous from Mr1,r2 (Rd) into Mt1,t2 (Rd).
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https://hdl.handle.net/11583/2509283
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