{
  "abstract": "We determine the exact strong-type Fourier restriction range for the unit sphere $\\mathbb{S}^{d-1}$ on the class of $O(d-k)\\times O(k)$-invariant functions, for every $d\\geq4$ and $2\\leq k\\leq d-2$. This includes the critical estimates beyond the biradial Stein--Tomas endpoint left open by Mandel and Oliveira e Silva. The proof combines a weighted $L^2$ estimate for extension from a circular arc with the full two-dimensional restriction theorem. An appendix gives a direct proof of the classically conjectured range for axially symmetric functions on the whole sphere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27967",
  "author_total": 4,
  "authors": [
    {
      "name": "Shinya Kinoshita"
    },
    {
      "name": "Juyoung Lee"
    },
    {
      "name": "Diogo Oliveira e Silva"
    },
    {
      "name": "Shobu Shiraki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ez1zmp8w3ctr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27967",
  "fulltext_url": null,
  "id": "4ez1zmp8w3ctr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27967",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223092036",
  "pdf_url": "https://arxiv.org/pdf/2610.27967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ez1zmp8w3ctr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Fourier restriction problem for biradial functions",
  "title_text": "The Fourier restriction problem for biradial functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/4ez1zmp8w3ctr",
  "venue": "arXiv",
  "versions": []
}