{
  "abstract": "We prove that the Toeplitz operator $T_{\\bar{z}+h}$ is invertible on the Bergman space provided that $|\\bar{z}+h|$ is bounded below by some positive constant on the open unit disk, where $h$ is in the disk algebra. This provides a general class of harmonic functions for which the answer to the Douglas question on the Bergman space is affirmative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22811",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiawei Wang"
    },
    {
      "name": "Xianfeng Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02dj0qwrc5nza.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22811",
  "fulltext_url": null,
  "id": "02dj0qwrc5nza",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22811",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7204186967",
  "pdf_url": "https://arxiv.org/pdf/2608.22811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02dj0qwrc5nza.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.22811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22811"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Douglas question for functions of the form $\\bar{z}+h$ with $h$ in the disk algebra",
  "title_text": "The Douglas question for functions of the form z̅+h with h in the disk algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/02dj0qwrc5nza",
  "venue": "arXiv",
  "versions": []
}