{"paper":{"title":"Some remarks on Fourier restriction estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jongchon Kim","submitted_at":"2017-02-04T03:29:41Z","abstract_excerpt":"We provide $L^p \\to L^q$ refinements on some Fourier restriction estimates obtained using polynomial partitioning. Let $S\\subset \\mathbb{R}^3$ be a compact $C^\\infty$ surface with strictly positive second fundamental form. We derive sharp $L^p(S) \\to L^q(\\mathbb{R}^3)$ estimates for the associated Fourier extension operator for $q> 3.25$ and $q\\geq 2p'$ from an estimate of Guth that was used to obtain $L^\\infty(S) \\to L^q(\\mathbb{R}^3)$ bounds for $q>3.25$. We present a slightly weaker result when $S$ is the hyperbolic paraboloid in $\\mathbb{R}^3$ based on the work of Cho and Lee. Finally, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01231","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"}