{
  "abstract": "Let $L$ be a nontrivial bounded linear functional on the Hardy space $H^p$ of the unit disc. We prove that if $0<p<1$ and if $f$ in the unit sphere of $H^p$ satisfies $L(f)=\\|L\\|$, then $f$ is an outer function. The proof is short and relies on a construction due to de Leeuw and Rudin. Our result complements work of Duren, Romberg, and Shields on the failure of the Hahn--Banach theorem for $H^p$. When applied to the special case $L_k(f) = f^{(k)}(0)/k!$ for $k=1,2,3,\\ldots$, it resolves two conjectures of the first-named author and Saksman and one conjecture of Suffridge.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21788",
  "author_total": 2,
  "authors": [
    {
      "name": "Ole Fredrik Brevig"
    },
    {
      "name": "Øistein Søvik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7drn56hrjmrbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21788",
  "fulltext_url": null,
  "id": "7drn56hrjmrbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21788",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7222623317",
  "pdf_url": "https://arxiv.org/pdf/2610.21788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7drn56hrjmrbr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extremals for linear functionals on $H^p$ are outer when $0<p<1$",
  "title_text": "Extremals for linear functionals on H^p are outer when 0<p<1",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7drn56hrjmrbr",
  "venue": "arXiv",
  "versions": []
}