{
  "abstract": "Let $Σ\\subset\\mathbb R^3$ be a compact $C^2$ hypersurface with nonvanishing Gaussian curvature. We prove the sharp matrix-dimension-independent Schatten-valued Stein--Tomas range \\[ R_Σ:L^p(\\mathbb R^3;S^a)\\longrightarrowγ(L^2(Σ),S^a), \\qquad 1<a<\\infty,\\quad 1\\le p\\le\\min\\{a,4/3\\}. \\] The core endpoint is $E_Σ:γ(L^2(Σ),S^4)\\to L^4(\\mathbb R^3;S^4)$. After squaring the quartic norm, multiplication lands in the Hilbert--Schmidt class. A local coarea argument splits resonant quartets according to the shorter adjacent frequency chord, producing a dimension-free row/column estimate for elliptic and hyperbolic curvature. We also show that Gaussian type $4/3$ alone does not characterize the corresponding endpoint for arbitrary Banach spaces. Applications include matrix Herglotz waves, a two-dimensional Schrödinger $L^4$ estimate, and free spectral-measure bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40044",
  "author_total": 2,
  "authors": [
    {
      "name": "R. Shahmurov"
    },
    {
      "name": "V. Shahmurov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ebcw8b277b0j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40044",
  "fulltext_url": null,
  "id": "3ebcw8b277b0j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40044",
  "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/2610.40044",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ebcw8b277b0j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40044",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40044"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$γ$-Valued Stein--Tomas Restriction for Schatten Classes",
  "title_text": "γ-Valued Stein--Tomas Restriction for Schatten Classes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3ebcw8b277b0j",
  "venue": "arXiv",
  "versions": []
}