{
  "abstract": "The Hilbert matrix operator $H$ is bounded on the standard weighted Bergman spaces $A^p_α,\\, p>α+2>1$. We examine the limiting case when $α=p-2$, and for $p\\leq 2$, we characterize the logarithmic modification of the standard weight needed for the domain $A^p_{v_{γ,p}}$ and codomain $A^p_{v_{β,p}}$ to ensure boundedness. In particular, we prove that $H:A^2_{\\log^γ} \\to A^2_{\\log^β}$ is bounded if and only if $γ-β\\geq 2$ and $γ>1$, solving an open problem posed by B. Karapetrović and M. Jevtić. We also settle the situation for $p>2$ in all cases, except when the logarithmic exponents $γ$ and $β$ satisfy $γ-β=p$. Moreover, we completely solve the same problem when the domain and codomain are certain weighted reflexive $\\ell^p$ spaces. All results are extended to the generalized Hilbert operator $H_g$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00252",
  "author_total": 1,
  "authors": [
    {
      "name": "David Norrbo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16x5bv0qf824c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00252",
  "fulltext_url": null,
  "id": "16x5bv0qf824c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00252",
  "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": "W7215802092",
  "pdf_url": "https://arxiv.org/pdf/2610.00252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16x5bv0qf824c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Hilbert matrix operator into the Bergman space",
  "title_text": "The Hilbert matrix operator into the Bergman space",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/16x5bv0qf824c",
  "venue": "arXiv",
  "versions": []
}