{
  "abstract": "We study the functional inequality \\[ f(r+s)\\le g(r)+αf(s) \\quad(r,s>0). \\] Here $g:(0,\\infty)\\to[0,\\infty)$ is a given decreasing function, $α$ is a constant such that $0<α<1$, and the problem is to determine whether the family of decreasing functions $f:(0,\\infty)\\to[0,\\infty)$ that satisfy this inequality is bounded above by some finite function on $(0,\\infty)$ and, if so, to find bounds for this function. We present a solution to this problem, and use it to give a new proof of a theorem of Domar on the uniform boundedness of certain families of subharmonic functions, in addition obtaining explicit bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08718",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Ransford"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42y5z97z1dghv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08718",
  "fulltext_url": null,
  "id": "42y5z97z1dghv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08718",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.08718",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42y5z97z1dghv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2607.08718",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08718"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A functional inequality related to Domar's uniform boundedness theorem",
  "title_text": "A functional inequality related to Domar's uniform boundedness theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/42y5z97z1dghv",
  "venue": "arXiv",
  "versions": []
}