{"paper":{"title":"Global and local maximizers for some Fourier extension estimates on the sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mateus Sousa, Valentina Ciccone","submitted_at":"2023-12-12T14:27:37Z","abstract_excerpt":"In this note, we study maximizers for Fourier extension inequalities on the sphere. We prove that constant functions are local maximizers for the $L^p(\\mathbb{S}^{d-1})$ to $L^p(\\mathbb{R}^d)$ Fourier extension estimates in the same range of exponents $p$ for which they are global maximizers for the $L^2(\\mathbb{S}^{d-1})$ to $L^p_{rad}L^2_{ang}(\\mathbb{R}^d)$ mixed-norm Fourier extension inequalities. Moreover, in the case of low dimensions, we improve the range of exponents for which constant functions are known to be the unique global maximizers for the $L^2(\\mathbb{S}^{d-1})$ to $L^p_{rad}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07309","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/2312.07309/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"}