{"paper":{"title":"Boundedness of Fourier Integral Operators on $\\mathcal{F} L^p$ spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elena Cordero, Fabio Nicola, Luigi Rodino","submitted_at":"2008-01-09T14:34:50Z","abstract_excerpt":"We study the action of Fourier Integral Operators (FIOs) of H{\\\"o}rmander's type on ${\\mathcal{F}} L^p({\\mathbb {R}}^d_{comp}$, $1\\leq p\\leq\\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded on these spaces when $p\\not=2$, the counterexample being given by any smooth non-linear change of variable. Here we show that FIOs of order $m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is proved to be sharp in every dimension $d\\geq1$, even for phases which are linear in the dual variables. The proofs make use of tools from tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1444","kind":"arxiv","version":3},"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"}