{
  "abstract": "In this paper we prove the sharp weak estimates for the Riesz potentials $$\\|I_{s}(f)\\|_{L^{\\frac{n}{n-s},\\infty}}\\leq γ_{n,s} v_n^{\\frac{n-s}{n}}\\frac{Γ(s/2)Γ((n+2-s)/2)}{Γ(n/2)}\\|f\\|_{L^1},~~ \\text{when}~~0<s<\\min\\{n,2\\}$$ and $$ \\|I_sf\\|_{L^{\\frac{n}{n-s},\\infty}} \\leq γ_{n,s}v_n^{\\frac{n-s}{n}}\\|f\\|_{L^1}, ~~\\text{when}~~2\\leq s<n,$$ where $γ_{n,s}=2^{-s}π^{-\\frac{n}{2}}\\frac{Γ(\\frac{n-s}{2})}{Γ(\\frac{s}{2})}$ and $v_n$ is the volume of the unit ball. The isoperimetric inequality for the Riesz capacity and the Newtonian isocapacitary inequality play a crucial role in our approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31043",
  "author_total": 2,
  "authors": [
    {
      "name": "Hanli Tang"
    },
    {
      "name": "Yaojun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b07chb29h4aj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31043",
  "fulltext_url": null,
  "id": "2b07chb29h4aj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31043",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7204867133",
  "pdf_url": "https://arxiv.org/pdf/2608.31043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b07chb29h4aj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.31043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp constants for weak estimates of the Riesz Potentials",
  "title_text": "Sharp constants for weak estimates of the Riesz Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2b07chb29h4aj",
  "venue": "arXiv",
  "versions": []
}