{"paper":{"title":"Dimension-free Fourier restriction inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Diogo Oliveira e Silva","submitted_at":"2024-12-05T07:45:03Z","abstract_excerpt":"Let ${{\\bf R}_{\\mathbb{S}^{d-1}}}(p\\to q)$ denote the best constant for the $L^p(\\mathbb{R}^d)\\to L^q(\\mathbb{S}^{d-1})$ Fourier restriction inequality to the unit sphere $\\mathbb{S}^{d-1}$, and let ${\\bf R}_{\\mathbb{S}^{d-1}} (p\\to q;\\textrm{rad})$ denote the corresponding constant for radial functions. We investigate the asymptotic behavior of the operator norms ${{\\bf R}_{\\mathbb{S}^{d-1}}}(p\\to q)$ and ${\\bf R}_{\\mathbb{S}^{d-1}} (p\\to q;\\textrm{rad})$ as the dimension $d$ tends to infinity. We further establish a dimension-free endpoint Stein-Tomas inequality for radial functions, togethe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03942","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/2412.03942/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"}