{
  "abstract": "We develop a structural theory of the Gaussian mixed-norm Fock spaces $\\mathcal F_α^{p,q}$, where $α>0$ and $0<p,q\\leq\\infty$, which separate angular $L^p$-means from radial Gaussian $L^q$-summability. We first prove the sharp circle-mean estimate $M_p(f,r)\\leq C_{α,q}(1+r)^{-\\frac{1}{q}} e^{\\fracα{2}r^2}\\lVert f\\rVert_{\\mathcal F_α^{p,q}}$, $r\\geq0$, where $M_p(f,r)$ denotes the angular $L^p$-mean of $f$ on the circle $\\lvert z\\rvert=r$ with the convention $\\frac{1}{\\infty}=0$, and show that the exponent $-\\frac{1}{q}$ is optimal. The proof is based on a local mass principle for convex Laplace-type exponents, which also yields an annular discretization of the mixed Gaussian norm. Using this discretization, we characterize the continuous embeddings between mixed-norm Fock spaces and obtain an atomic decomposition in terms of normalized Fock kernels, with coefficients belonging to a corresponding annular mixed sequence space. We further characterize Carleson and vanishing Carleson measures and identify the continuous duals in the Banach, quasi-Banach, and endpoint regimes. For $p<1$, the atomic decomposition relies on a quantitative re-centering theorem that controls expansions of normalized Fock kernels under perturbations of their centers. This theorem is of independent interest even for the Hilbert Fock space $\\mathcal F_α^{2}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26821",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiang Fang"
    },
    {
      "name": "Pham Trong Tien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh9597mkgd2ym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26821",
  "fulltext_url": null,
  "id": "bh9597mkgd2ym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26821",
  "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": "W7214230305",
  "pdf_url": "https://arxiv.org/pdf/2609.26821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh9597mkgd2ym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Gaussian Mixed-Norm Theory for Fock Spaces",
  "title_text": "Sharp Gaussian Mixed-Norm Theory for Fock Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/bh9597mkgd2ym",
  "venue": "arXiv",
  "versions": []
}