{
  "abstract": "We allow the exponent $α$ that defines the positive Bergman operator on the upper half-plane to differ from the exponent $γ$ that defines the underlying weighted Lebesgue spaces. In this setting, we prove a sharp weak-type off-diagonal weighted inequality, with explicit and best-possible dependence on the Békollé--Bonami characteristic of the weight. We then deduce strong-type off-diagonal inequalities for the same operator. The key new tool is an off-diagonal extrapolation theorem, adapted to allow a change in the power of the distance to the boundary along the way.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01159",
  "author_total": 1,
  "authors": [
    {
      "name": "Benoit F. Sehba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e56fpmqc69jh7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01159",
  "fulltext_url": null,
  "id": "e56fpmqc69jh7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01159",
  "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.CA"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7172377175",
  "pdf_url": "https://arxiv.org/pdf/2608.01159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e56fpmqc69jh7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.01159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case",
  "title_text": "Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/e56fpmqc69jh7",
  "venue": "arXiv",
  "versions": []
}