{
  "abstract": "Let $μ$ be a finite positive Borel measure on $[0,1)$ and let $γ>0$. We establish sharp mapping criteria for the generalized Cesàro operator \\begin{equation*} \\mathcal C_{μ,γ}f(z) =\\sum_{n=0}^\\infty μ_n \\left(\\sum_{k=0}^n \\frac{Γ(n-k+γ)}{Γ(γ)(n-k)!}a_k\\right)z^n,\\qquad z\\in \\mathbb{D},\\end{equation*} between Hardy spaces, including the source and target $H^\\infty$ endpoints. For $0<p<q<\\infty$, for $0<p=q<1$, and for $0<p\\le1$ with $q=\\infty$, the boundedness of $ \\mathcal C_{μ,γ}: H^p \\to H^q$ is equivalent to $μ$ being a $(γ+1/p-1/q)$-Carleson measure, without further restrictions on $γ$. For $1\\le q<p\\le\\infty$, set $1/r=1/q-1/p$. In this range, boundedness and compactness are equivalent to \\[ \\int_0^1 \\left(\\frac{μ([t,1))}{(1-t)^{γ-1/r}}\\right)^r \\frac{dt}{1-t}<\\infty. \\] This condition is also equivalent to $F_{μ,γ}\\in H^r$ and to $\\sum_{n\\ge0}(n+1)^{rγ-2}μ_n^r<\\infty$, where $F_{μ,α}=\\mathcal C_{μ,α}(1)$ and $μ_n=\\int_{[0,1)}t^n\\,dμ(t)$. For $1<p<\\infty$, boundedness and compactness from $H^p$ to $H^\\infty$ are characterized by the shifted condition $F_{μ,γ+1}\\in H^{p'}$, where $p'=p/(p-1)$. We therefore obtain a complete boundedness classification of the generalized Cesàro operators $\\mathcal C_{μ,γ}$ between Hardy spaces $H^p$ and $H^q$ for the full range $0<p,q\\le\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19725",
  "author_total": 2,
  "authors": [
    {
      "name": "Pengcheng Tang"
    },
    {
      "name": "Huayou Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vc13f9pf688e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19725",
  "fulltext_url": null,
  "id": "7vc13f9pf688e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19725",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213606547",
  "pdf_url": "https://arxiv.org/pdf/2609.19725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vc13f9pf688e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Complete mapping criteria for generalized Cesàro operators between Hardy spaces",
  "title_text": "Complete mapping criteria for generalized Cesàro operators between Hardy spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/7vc13f9pf688e",
  "venue": "arXiv",
  "versions": []
}