{
  "abstract": "Classical Stein--Tomas restriction controls a Fourier transform on a curved surface, but the estimate changes when its values lie in a Banach space. We determine the sharp Lorentz threshold at the critical exponent $4/3$: for coefficients in $\\ell_D^{4/3,q}$, the optimal Gaussian restriction constant grows like $(1+\\log D)^{|3/4-1/q|}$. A multiscale wave-packet construction proves sharpness, including the delicate index $q=2$. The same threshold holds for fractional Gaussian noise, while Gaussian type and cotype alone do not distinguish the positive and negative cases. As a dispersive consequence, we establish a sharp Lorentz-channel spacetime estimate for linear capillary waves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01232",
  "author_total": 2,
  "authors": [
    {
      "name": "R. Shahmurov"
    },
    {
      "name": "V. Shahmurov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85ynjv6ez0134.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01232",
  "fulltext_url": null,
  "id": "85ynjv6ez0134",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01232",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01232",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85ynjv6ez0134.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01232",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01232"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Lorentz Threshold in Fourier Restriction",
  "title_text": "The Lorentz Threshold in Fourier Restriction",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/85ynjv6ez0134",
  "venue": "arXiv",
  "versions": []
}