{
  "abstract": "Let $Ω=Ω^+\\subset \\mathbb{R}^{n+1}$ be a bounded open set with $n$-Ahlfors regular boundary and let $Ω^-=\\mathbb{R}^{n+1}\\setminus\\overline{Ω^+}$. For $x\\in\\partialΩ$, $r>0$, define \\begin{equation*} \\varepsilon_{n,Ω}(x,r):=\\frac{1}{r^n} \\inf_{H^+}\\mathcal{H}^n\\left(((\\partial B(x,r)\\cap H^+)\\setminus Ω^+) \\cup ((\\partial B(x,r)\\cap H^-)\\setminus Ω^-)\\right), \\end{equation*} where $\\mathcal{H}^n$ stands for $n$-dimensional Hausdorff measure and the infimum is taken over all open affine half-spaces $H^+$ such that $x\\in \\partial H^+$. Here $H^-=\\mathbb{R}^{n+1}\\setminus \\overline{H^+}$. In this work we prove that $Ω$ is a $C^{1,α}$ open set, with $0<α<1$, if and only if there exists some constant $C>0$ such that $\\varepsilon_{n,Ω}(x,r)\\leq C\\,r^α$ for all $x\\in\\partialΩ$ and all $0<r\\leq \\mathrm{diam}(\\partialΩ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20207",
  "author_total": 2,
  "authors": [
    {
      "name": "Xavier Tolsa"
    },
    {
      "name": "Tobias Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gwkp6v0f54p2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20207",
  "fulltext_url": null,
  "id": "2gwkp6v0f54p2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20207",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222207113",
  "pdf_url": "https://arxiv.org/pdf/2610.20207",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gwkp6v0f54p2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterization of $C^{1,α}$-domains in terms of Carleson-type $\\varepsilon$-coefficients",
  "title_text": "Characterization of C^1,α-domains in terms of Carleson-type ε-coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2gwkp6v0f54p2",
  "venue": "arXiv",
  "versions": []
}