{
  "abstract": "For $\\mathcal H:\\mathcal B^α\\to\\mathcal B^α$ with $1<α<2$, we obtain an exact norm representation. In particular, the norm is given by an explicit Gamma-function formula for $1<α\\leq3/2$, whereas for $3/2<α<2$ it strictly exceeds the corresponding Gamma-function expression. For $\\mathcal H:\\mathcal B^α\\to\\mathcal B^α_{\\log}$, we determine the exact norm: it is equal to $3/2$ for $1<α\\leq4/3$ and is given by an explicit Gamma-function formula for $4/3<α<2$. We also determine the exact norm of $\\mathcal H:H^1\\to H^1_{\\log}$ and show that it is equal to $π$. Finally, for $0<α<1$, we determine the exact norm of $\\mathcal H:H^\\infty_α\\to\\mathcal B^{α+1}$, which is given by an explicit Gamma-function formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27812",
  "author_total": 4,
  "authors": [
    {
      "name": "Puyu Cui"
    },
    {
      "name": "Zhaopeng Lin"
    },
    {
      "name": "Yufeng Lu"
    },
    {
      "name": "Shanli Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73dze1wstwdve.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27812",
  "fulltext_url": null,
  "id": "73dze1wstwdve",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27812",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214203220",
  "pdf_url": "https://arxiv.org/pdf/2609.27812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73dze1wstwdve.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2609.27812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Norms of the Hilbert Matrix Operator on Some Analytic Function Spaces",
  "title_text": "Norms of the Hilbert Matrix Operator on Some Analytic Function Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/73dze1wstwdve",
  "venue": "arXiv",
  "versions": []
}