{
  "abstract": "We establish an endpoint weighted Fourier estimate under a vanishing restriction condition on the unit sphere. Let $n \\geq 2$ and $p_c = 2(n+1)/(n+3)$. We prove that every $f \\in L^{p_c}(\\mathbb{R}^n)$ with zero spherical Fourier restriction satisfies $$ \\left\\| \\bigl|1-|ξ|^2\\bigr|^{-1/2}\\widehat{f}(ξ) \\right\\|_{L^2(\\mathbb{R}^n)} \\leq C_n \\|f\\|_{L^{p_c}(\\mathbb{R}^n)}, $$ where the restriction condition is understood through the continuous Tomas--Stein restriction operator. This result gives a negative answer to Goldberg's counterexample-existence question and supplies a missing endpoint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31353",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenjuan Li"
    },
    {
      "name": "Manli Song"
    },
    {
      "name": "Hongqiang Wang"
    },
    {
      "name": "Huiju Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6gvb2enkqt1nk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31353",
  "fulltext_url": null,
  "id": "6gvb2enkqt1nk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31353",
  "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": "W7223359524",
  "pdf_url": "https://arxiv.org/pdf/2610.31353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6gvb2enkqt1nk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Endpoint weighted Fourier estimate with vanishing spherical trace",
  "title_text": "Endpoint weighted Fourier estimate with vanishing spherical trace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/6gvb2enkqt1nk",
  "venue": "arXiv",
  "versions": []
}