{
  "abstract": "We characterize compact Toeplitz operators with bounded complex-valued symbols on the Bergman space of a bounded strongly pseudoconvex domain with $C^2$ boundary. For any fixed $R>0$, the operator $T_f$ is compact if and only if the Euclidean-volume averages of $f$ over Bergman geodesic balls of radius $R$ tend to zero at the boundary. This answers Zhu's fixed-radius question affirmatively on the unit ball. On the polydisc $\\mathbb D^n$, $n\\ge2$, averages over products of Bergman discs of fixed radii characterize compactness, whereas averages over genuine Bergman geodesic balls need not. For every sufficiently small fixed radius, we construct a bounded real-valued symbol, smooth in the domain, whose geodesic-ball averages tend to zero along every sequence approaching the boundary, while its Berezin transform converges to a positive value along one such sequence. Boundary scaling reduces the strongly pseudoconvex case to a uniqueness problem for fixed-radius ball averages on complex hyperbolic space. We prove the required uniqueness theorem under a sharp decay condition expressed in terms of a Busemann height function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22893",
  "author_total": 2,
  "authors": [
    {
      "name": "Pan Ma"
    },
    {
      "name": "Zhaoxi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4krdhaatm0txm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22893",
  "fulltext_url": null,
  "id": "4krdhaatm0txm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22893",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7222946816",
  "pdf_url": "https://arxiv.org/pdf/2610.22893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4krdhaatm0txm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Compact Toeplitz Operators and the Geometry of Fixed-Radius Averages",
  "title_text": "Compact Toeplitz Operators and the Geometry of Fixed-Radius Averages",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/4krdhaatm0txm",
  "venue": "arXiv",
  "versions": []
}