{
  "abstract": "We introduce a class of plurisubharmonic weights on \\mathbb C^n and develop a theory of the associated weighted Fock spaces F_φ^p. The curvature assumptions are imposed on a \\mathcal C^2-regularization at bounded distance from the original weight. Thus the original weight need not be smooth or strictly plurisubharmonic, and, even when it is of class \\mathcal C^2, its complex Hessian eigenvalues need not be uniformly comparable. This provides a counterpart of Christ's doubling theory in several complex variables. We establish a global upper estimate with decay away from the diagonal and a uniform lower estimate near the diagonal for the weighted Bergman kernel. These estimates yield L^p bounds for the kernel functions, boundedness of the Bergman projection, and duality and complex interpolation for the associated Fock spaces. For a certain class of weights beyond the uniformly controlled curvature setting, we construct an integral solution operator for the \\bar\\partial equation and establish scale-adapted weighted L^p estimates for 1\\leq p\\leq\\infty. As an application, for all 1\\leq p,q<\\infty, we characterize the boundedness and compactness of Hankel operators from F_φ^p to L_φ^q with possibly unbounded symbols in terms of weighted IDA spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26810",
  "author_total": 3,
  "authors": [
    {
      "name": "Guijun Liu"
    },
    {
      "name": "Xiaofeng Wang"
    },
    {
      "name": "Zhicheng Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e01hhrwvnwsqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26810",
  "fulltext_url": null,
  "id": "e01hhrwvnwsqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26810",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214224414",
  "pdf_url": "https://arxiv.org/pdf/2609.26810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e01hhrwvnwsqg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Bergman Kernels and Hankel Operators on Weighted Fock Spaces in Several Complex Variables",
  "title_text": "Bergman Kernels and Hankel Operators on Weighted Fock Spaces in Several Complex Variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/e01hhrwvnwsqg",
  "venue": "arXiv",
  "versions": []
}