{
  "abstract": "Let $μ$ be a positive Borel measure on $[0,1)$ and $ω$ a radial weight. In this paper we consider the Cesàro-type operator $C_{μ,ω}$ induced by the reproducing kernel $B^ω$ of the weighted Bergman space $A^2_ω$, given by $$ C_{μ,ω}(f)(z)=\\int_{0}^{1}f(tz)B^ω_t(z)\\,dμ(t), \\quad z \\in \\mathbb{D}, $$ for functions $f$ analytic in $\\mathbb{D}$. Under the assumption that $ω$ satisfies a natural doubling property, we study the boundedness of $C_{μ,ω}$ acting on several spaces of analytic functions, including Hardy spaces $H^p$ and weighted Bergman spaces $A^p_ν$. For $0<p,q<\\infty$ and a two-sided doubling weight $ν$, we completely characterize when $C_{μ,ω}: H^p \\to H^q$ and $C_{μ,ω}: A^p_ν \\to A^q_ν$ are bounded in terms of the interplay of tail integrals or moments of the inducing weights and the measure $μ$. Many of the results obtained are new even in the setting of standard weights or when the Bergman reproducing kernel is replaced by the Cauchy kernel. In addition, we consider $C_{μ,ω}$ acting on $H^{\\infty}$, Korenblum spaces and weighted Hardy spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21657",
  "author_total": 2,
  "authors": [
    {
      "name": "Oscar Blasco"
    },
    {
      "name": "Atte Pennanen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58200zh5qyjc2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21657",
  "fulltext_url": null,
  "id": "58200zh5qyjc2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21657",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213902589",
  "pdf_url": "https://arxiv.org/pdf/2609.21657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58200zh5qyjc2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21657"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Cesàro operator induced by a Bergman kernel",
  "title_text": "Cesàro operator induced by a Bergman kernel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/58200zh5qyjc2",
  "venue": "arXiv",
  "versions": []
}