{
  "abstract": "In this paper, a complete characterization of the boundedness, compactness, norm and essential norm of the differential Hilbert operator $\\mathcal{H}_2:A^2_α\\to A^2_β$ is obtained. More precisely, $\\mathcal H_2:A^2_α\\to A^2_β$ is bounded if and only if $-1<α<0$ and $β\\geqα+2$ and it is compact if and only if $-1<α<0$ and $β>α+2$. The norm and essential norm of $ \\|\\mathcal H_2\\|_{A^2_α\\to A^2_β}$ are also investigated. In particular, when $β=α+2$, \\[ \\|\\mathcal H_2\\|_{A^2_α\\to A^2_{α+2}} =\\|\\mathcal H_2\\|_{\\mathrm e,A^2_α\\to A^2_{α+2}} =\\frac{π\\sqrt{(α+2)(α+3)}} {\\sin(π(α+2)/2)},\\qquad -1<α<0. \\] When $β>α+2$, $\\|\\mathcal H_2\\|_{\\mathrm e,A^2_α\\to A^2_β}=0$. Furthermore, for every $1\\leq p<\\infty$, the operator $\\mathcal H_2$ belongs to the Schatten class $\\mathcal S_p$ if and only if it is compact.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05672",
  "author_total": 2,
  "authors": [
    {
      "name": "Songxiao Li"
    },
    {
      "name": "Mengmeng Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9wr034167rqx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05672",
  "fulltext_url": null,
  "id": "d9wr034167rqx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05672",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7220711893",
  "pdf_url": "https://arxiv.org/pdf/2610.05672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9wr034167rqx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Differential Hilbert Operator Between Weighted Bergman Spaces",
  "title_text": "The Differential Hilbert Operator Between Weighted Bergman Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/d9wr034167rqx",
  "venue": "arXiv",
  "versions": []
}