{"paper":{"title":"Restriction of Fourier transforms to curves and related oscillatory integrals","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Daniel M. Oberlin, Jong-Guk Bak","submitted_at":"2006-12-24T14:03:12Z","abstract_excerpt":"We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in $\\Bbb R^d$, $d\\ge 3$, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in $\\Bbb R^d$ we obtain sharp uniform $L^p\\to L^q$ bounds with respect to affine arclength measure, thereby resolving a problem of Drury and Marshall."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612752","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0612752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}