{
  "abstract": "We study weighted Bergman spaces of quasiregular mappings on the unit ball in $\\mathbb{R}^n$, with weight $(1-|x|)^α$, $α>-1$. For every fixed distortion bound $K\\ge1$ and every $p>0$, we characterize Bergman integrability by averaged derivatives. We also give geometric conditions under which integration over a subset, or against another measure, controls the full Bergman integral. When $K$ is sufficiently large, the dominating sets are precisely the relatively dense sets. For comparison, we determine the dominating sets for the Möbius class $K=1$ in dimensions $n\\ge3$. At the critical exponent $p=n+α$, its domination criterion differs from that for every fixed $K>1$. Our results extend aspects of the Bergman theory developed by Nolder~\\cite{Nolder90} and by Oleinik and Vuorinen~\\cite{OV}, and complement the recent work of Adamowicz and González~\\cite{AG21,AG25} and Adamowicz and Caamaño~\\cite{AC} on quasiregular Hardy spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14837",
  "author_total": 1,
  "authors": [
    {
      "name": "Suman Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wmnppx8ek5n1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14837",
  "fulltext_url": null,
  "id": "2wmnppx8ek5n1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14837",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7221796300",
  "pdf_url": "https://arxiv.org/pdf/2610.14837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wmnppx8ek5n1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Averaged derivatives and reverse inequalities in quasiregular Bergman spaces",
  "title_text": "Averaged derivatives and reverse inequalities in quasiregular Bergman spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2wmnppx8ek5n1",
  "venue": "arXiv",
  "versions": []
}