{"paper":{"title":"Boundedness of Schroedinger type propagators on modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Elena Cordero, Fabio Nicola","submitted_at":"2008-07-15T14:16:23Z","abstract_excerpt":"It is known that Fourier integral operators arising when solving Schr\\\"odinger-type operators are bounded on the modulation spaces $\\cM^{p,q}$, for $1\\leq p=q\\leq\\infty$, provided their symbols belong to the Sj\\\"ostrand class $M^{\\infty,1}$. However, they generally fail to be bounded on $\\cM^{p,q}$ for $p\\not=q$. In this paper we study several additional conditions, to be imposed on the phase or on the symbol, which guarantee the boundedness on $\\cM^{p,q}$ for $p\\not=q$, and between $\\cM^{p,q}\\to\\cM^{q,p}$, $1\\leq q< p\\leq\\infty$. We also study similar problems for operators acting on Wiener a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.2380","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}