{
  "abstract": "We obtain improved Fourier restriction and Kakeya maximal estimates in $\\mathbb R^4$. More precisely, by proving the two-ends incidence estimates $\\mathbf{TE}\\left(\\frac{269}{89},\\frac{179}{89},\\frac{493}{534}\\right)$ and $\\mathbf{TE}(3.06\\ldots,3.06\\ldots,0.94\\ldots)$, we extend the restriction range to $p>2+ \\frac{356}{447}$ and the Kakeya maximal estimate up to dimension $3.06056$. The implications to the known lower-bounds for the Hausdorff dimension of Kakeya sets in $\\mathbb{R}^4$ and the Bochner--Riesz conjecture are also studied.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06181",
  "author_total": 1,
  "authors": [
    {
      "name": "Tiago Moreira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bkmv476dyya6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06181",
  "fulltext_url": null,
  "id": "2bkmv476dyya6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06181",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220746339",
  "pdf_url": "https://arxiv.org/pdf/2610.06181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bkmv476dyya6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.06181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Refinements on the Restriction and Kakeya problems range in $\\mathbb{R}^4$",
  "title_text": "Refinements on the Restriction and Kakeya problems range in ℝ^4",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2bkmv476dyya6",
  "venue": "arXiv",
  "versions": []
}