{
  "abstract": "For integers $n\\ge1$ and $N\\ge0$, let $\\mathbf g=(g_0,\\ldots,g_N)$ be a vector of entire functions. We consider the generalized integral operator \\ [T_{\\mathbf g}^{(n,N)}f =I^n\\!\\left(\\sum_{j=0}^N g_jf^{(j)}\\right), \\qquad (Ih)(z)=\\int_0^z h(w)\\dd w. \\] We characterize its boundedness and compactness between Fock--Sobolev spaces $\\F_m^p$ and $\\F_\\ell^q$, where $0<p,q<\\infty$ and $m,\\ell\\ge0$ are integers. The coefficients of critical total degree determine the operator modulo compact operators and yield essential-norm estimates. In the Hilbert case, a Laurent Toeplitz representation gives the exact essential norm, a Fredholm criterion and an index formula. As an application, we obtain conditions for solutions of linear differential equations to belong to Fock--Sobolev spaces, including a necessary and sufficient polynomial zero condition in the Hilbert case. For entire functions $u_0,\\ldots,u_N$ and $φ$, we also characterize boundedness, compactness and essential norms of the operators \\[ L_{\\mathbf u,φ}^{(N)}f =\\sum_{j=0}^N u_j\\,f^{(j)}\\circφ. \\] The proofs use Carleson measure characterizations for finite sums of weighted differentiation operators on Fock--Sobolev spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01959",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianxiang Dong"
    },
    {
      "name": "Shibo Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vkpwmzt1f2b1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01959",
  "fulltext_url": null,
  "id": "9vkpwmzt1f2b1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01959",
  "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.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vkpwmzt1f2b1.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01959"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Carleson Measures and Integral Operators on Fock--Sobolev Spaces",
  "title_text": "Carleson Measures and Integral Operators on Fock--Sobolev Spaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9vkpwmzt1f2b1",
  "venue": "arXiv",
  "versions": []
}