{"paper":{"title":"Sharp mixed norm spherical restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Diogo Oliveira e Silva, Emanuel Carneiro, Mateus Sousa","submitted_at":"2017-10-28T01:10:58Z","abstract_excerpt":"Let $d\\geq 2$ be an integer and let $2d/(d-1) < q \\leq \\infty$. In this paper we investigate the sharp form of the mixed norm Fourier extension inequality \\begin{equation*} \\big\\|\\widehat{f\\sigma}\\big\\|_{L^q_{{\\rm rad}}L^2_{{\\rm ang}}(\\mathbb{R}^d)} \\leq {\\bf C}_{d,q}\\, \\|f\\|_{L^2(\\mathbb{S}^{d-1},{\\rm d}\\sigma)}, \\end{equation*} established by L. Vega in 1988. Letting $\\mathcal{A}_d \\subset (2d/(d-1), \\infty]$ be the set of exponents for which the constant functions on $\\mathbb{S}^{d-1}$ are the unique extremizers of this inequality, we show that: (i) $\\mathcal{A}_d$ contains the even integer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10365","kind":"arxiv","version":3},"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/1710.10365/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"}