{
  "abstract": "We study a weighted Fourier capacity attached to compact sets, $ c_{p,k}(K)=\\inf\\left\\{\\|k\\widehat u\\|_{L^p(\\mathbb{R}^d)}:u\\in C_0^\\infty(\\mathbb{R}^d),\\ u\\geq 1 \\text{ on } K\\right\\},$ where $k$ is a positive tempered weight. The paper develops complementary upper and lower estimates for this quantity. The upper bounds are obtained from Frostman data, Fourier restriction estimates, and Bessel-potential majorants, which together provide admissible smooth majorants of the compact set. The lower bounds follow from a dual testing argument against positive measures supported on $K$, yielding estimates in terms of the weighted $L^{p'}$ size of their Fourier transforms. For sets of positive Lebesgue measure, testing with $χ_K\\,\\mathrm{d}x$ connects the capacity with the weighted integrability of $\\widehat{χ_K}$. A Lebedev-type Sobolev criterion then gives non-triviality ranges governed by the upper Minkowski dimension of $\\partial K$ and the growth of the weight. We also record consequences for Ahlfors-David regular sets and positive-measure Cantor-type examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20800",
  "author_total": 2,
  "authors": [
    {
      "name": "Rodrigo Leon"
    },
    {
      "name": "Vicente Vergara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/059cebss6f04w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20800",
  "fulltext_url": null,
  "id": "059cebss6f04w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20800",
  "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": "W7222548548",
  "pdf_url": "https://arxiv.org/pdf/2610.20800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/059cebss6f04w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20800"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted Fourier capacities and Frostman restriction estimates",
  "title_text": "Weighted Fourier capacities and Frostman restriction estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/059cebss6f04w",
  "venue": "arXiv",
  "versions": []
}