{
  "abstract": "Given a radial doubling weight $μ$ on the unit disk $\\mathbb{D}$ and $f(z)=\\sum_{n=0}^\\infty \\hat{f}(n)z^n\\in\\mathcal{H}(\\mathbb{D})$, the fractional derivative of $f$ induced by $μ$ is $$ D^μ(f)(z) = \\sum_{n=0}^\\infty \\frac{\\hat{f}(n)}{μ_{2n+1}}z^n, $$ where $μ_{2n+1}=\\int_0^1 r^{2n+1}μ(r)\\,dr$ are the odd moments of $μ$. The fractional integral of $f$ induced by $μ$ is $I^μ(f)(z)=\\sum_{n=0}^\\infty μ_{2n+1}\\hat{f}(n)z^n$. We study the fractional Volterra-type operator $$ V_{μ,g}(f)(z)=I^μ(f\\cdot D^μ(g))(z),\\quad f\\in\\mathcal{H}(\\mathbb{D}), $$ with symbol $g\\in\\mathcal{H}(\\mathbb{D})$, introduced by Bellavita, Moreno, Nikolaidis and Peláez. First, we estimate the essential norm of $V_{μ,g}$ acting on $H^p$ and $A^p_α$. Later, we study the same questions for $V_{μ,g}:H^p\\to H^q$ and $V_{μ,g}:A^p_α\\to A^q_α$, characterizing their boundedness and compactness and estimating their essential norms for all $0<p,q<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37548",
  "author_total": 1,
  "authors": [
    {
      "name": "Álvaro Miguel Moreno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1tyzgxveqpfm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37548",
  "fulltext_url": null,
  "id": "f1tyzgxveqpfm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37548",
  "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"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7224090456",
  "pdf_url": "https://arxiv.org/pdf/2610.37548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1tyzgxveqpfm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Essential norms of fractional Volterra-type operators",
  "title_text": "Essential norms of fractional Volterra-type operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/f1tyzgxveqpfm",
  "venue": "arXiv",
  "versions": []
}