{
  "abstract": "We show that for every $n\\ge2$, $p>2$, and positive integer $m$, there exists a finite-volume pseudoconvex domain $D\\subset\\mathbb C^n$ with real-analytic strongly pseudoconvex boundary whose $p$-Bergman space $A^p(D)$ has dimension $m$. These domains admit smooth strictly plurisubharmonic exhaustions and satisfy $H^\\infty(D)=\\mathbb C$ and $\\dim A^s(D)=\\infty$ for every $0<s\\le2$. Moreover, for every finite $s\\ge p$, we have $\\dim A^s(D)=\\lceil pm/s\\rceil$. As an application, we show that the Bergman projection fails to map $\\mathcal{C}_c^\\infty(D)$ into $A^p(D)$ and admits no bounded extension to $L^s(D)$ or $L^{s/(s-1)}(D)$ for any finite $s\\ge p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00501",
  "author_total": 3,
  "authors": [
    {
      "name": "Shreedhar Bhat"
    },
    {
      "name": "Soumya Ganguly"
    },
    {
      "name": "Achinta Kumar Nandi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3hraax1jtxqaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00501",
  "fulltext_url": null,
  "id": "3hraax1jtxqaz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00501",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3hraax1jtxqaz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strongly Pseudoconvex Domains with Finite Dimensional $p$-Bergman Spaces",
  "title_text": "Strongly Pseudoconvex Domains with Finite Dimensional p-Bergman Spaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3hraax1jtxqaz",
  "venue": "arXiv",
  "versions": []
}