{"paper":{"title":"Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Fabio Nicola","submitted_at":"2008-05-27T13:53:17Z","abstract_excerpt":"We carry on the study of Fourier integral operators of H{\\\"o}rmander's type acting on the spaces $(\\mathcal{F}L^p)_{comp}$, $1\\leq p\\leq\\infty$, of compactly supported distributions whose Fourier transform is in $L^p$. We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank $r$ of the Hessian of the phase $\\Phi(x,\\eta)$ with respect to the space variables $x$. Indeed, we show that operators of order $m=-r|1/2-1/p|$ are bounded on $(\\mathcal{F}L^p)_{comp}$, if the mapping $x\\longmapsto\\nabla_x\\Phi(x,\\eta)$ is constant on the fibers, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4122","kind":"arxiv","version":1},"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"}