{
  "abstract": "In this paper, we study the Cesàro-type operator $$ \\Ces_{μ,β}f(z)=\\int_{[0,1)}\\frac{f(tz)}{(1-tz)^β}\\,dμ(t), $$ where \\(μ\\) is a positive Borel measure on \\([0,1)\\) and \\(β>0\\). For \\(0<p,q<\\infty\\) and radial doubling weights \\(ω_1,ω_2\\), we prove that \\(\\Ces_{μ,β}:\\AL_p^q(ω_1)\\to\\AL_p^q(ω_2)\\) is bounded if and only if $$ μ([0,1))+\\sup_{1/2\\le r<1}\\frac{μ([r,1))}{(1-r)^β}\\left(\\frac{\\whatω_2(r)}{\\whatω_1(r)}\\right)^{1/p}<\\infty, $$ and its norm is comparable to this quantity. For standard weights, our result extends \\cite{BlascoMas2026,GalanopoulosSiskakisZhao2025} to the full range $0<p=q<\\infty$. We further characterize compactness and the essential norm on average radial integrability spaces induced by doubling weights.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24216",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiaxin Pan"
    },
    {
      "name": "Cezhong Tong"
    },
    {
      "name": "Zixing Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2522wrnfx9v79.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24216",
  "fulltext_url": null,
  "id": "2522wrnfx9v79",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24216",
  "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": "W7214047319",
  "pdf_url": "https://arxiv.org/pdf/2609.24216",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2522wrnfx9v79.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24216",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24216"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Cesàro-type operators on average radial integrability spaces induced by doubling weights",
  "title_text": "Cesàro-type operators on average radial integrability spaces induced by doubling weights",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2522wrnfx9v79",
  "venue": "arXiv",
  "versions": []
}