{
  "abstract": "We study the truncated Dirichlet functional \\[ Φ_n (f) = \\sum_{k = 1}^n k |a_k|^2, \\quad f(z) = \\sum_{k = 0}^\\infty a_k z^k, \\] when $f$ belongs to the Bloch space. If $n \\geq 27$, we find a normalized Bloch function $f_n$ such that \\[ Φ_n (f_n) > n B_n^2, \\] where $B_n = \\max \\{ |a_n| : \\| f \\|_{\\mathcal{B}} = 1 \\}$, thus proving that an inequality by Kayumov and Wirths cannot be extended to large values of $n$. Nevertheless, we show that the inequality $Φ_n(f) \\leq n B_n^2$ holds for all normalized functions when $n \\leq 9$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41534",
  "author_total": 3,
  "authors": [
    {
      "name": "Iason Efraimidis"
    },
    {
      "name": "Adrián Llinares"
    },
    {
      "name": "Alejandro Mas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11jnn7qhqw4r4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41534",
  "fulltext_url": null,
  "id": "11jnn7qhqw4r4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41534",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11jnn7qhqw4r4.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Truncated Dirichlet estimates for Bloch functions",
  "title_text": "Truncated Dirichlet estimates for Bloch functions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/11jnn7qhqw4r4",
  "venue": "arXiv",
  "versions": []
}