{"paper":{"title":"Endpoint estimates for one-dimensional oscillatory integral operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lechao Xiao","submitted_at":"2016-02-18T02:34:57Z","abstract_excerpt":"The one-dimensional oscillatory integral operator associated to a real analytic phase $S$ is given by $$ T_\\lambda f(x) =\\int_{-\\infty}^\\infty e^{i\\lambda S(x,y)} \\chi(x,y) f(y) dy. $$ In this paper, we obtain a complete characterization for the mapping properties of $T_\\lambda $ on $L^p(\\mathbb R)$ spaces, namely we prove that $\\|T_\\lambda\\|_p \\lesssim |\\lambda|^{-\\alpha}\\|f\\|_p$ for some $\\alpha>0$ if and only if the point $(\\frac 1 {\\alpha p} , \\frac 1 {\\alpha p'})$ lies in the reduced Newton polygon of $S$, and this estimate is sharp if and only if it lies on the reduced Newton diagram."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05663","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"}