{
  "abstract": "The Fock--Bargmann projection \\(P_t\\) is initially an orthogonal projection on a Gaussian Hilbert space. We characterize the boundedness and compactness of \\[ P_t:L_α^{p_1,q_1}\\longrightarrow \\mathcal F_β^{p_2,q_2} \\] and of its associated maximal projection \\[ P_t^+:L_α^{p_1,q_1}\\longrightarrow L_β^{p_2,q_2} \\] for all \\(t,α,β>0\\) and \\(0<p_1,q_1,p_2,q_2\\le\\infty\\). Set \\[ Δ(t;α,β):=t^2-2βt+αβ, \\qquad d(p,q):=\\frac1q-\\frac1p. \\] For both operators, boundedness holds exactly when \\(p_1,q_1\\ge1\\) and either \\(Δ(t;α,β)<0\\), or \\(Δ(t;α,β)=0\\) with \\[ q_1\\le q_2, \\qquad d(p_2,q_2)\\le d(p_1,q_1). \\] Both operators are compact exactly when \\(p_1,q_1\\ge1\\) and either \\(Δ(t;α,β)<0\\), or \\(Δ(t;α,β)=0\\) with both of the above boundary inequalities strict. Thus boundedness forces the source exponents into the Banach range, whereas when \\(Δ(t;α,β)<0\\), every target exponent is admissible, including quasi-Banach ones. Annular discretization reduces the problem to drifted Gaussian sequence operators, whose comparison with diagonal sequence operators yields the endpoint criteria and quantitative tail estimates. A dilation--multiplier transfer gives corresponding results for Gaussian-twisted Fock operators, including Berezin transforms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41461",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiang Fang"
    },
    {
      "name": "Pham Trong Tien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58nfjazts0v8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41461",
  "fulltext_url": null,
  "id": "58nfjazts0v8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41461",
  "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/2610.41461",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58nfjazts0v8m.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41461",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41461"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fock Projections between Gaussian Mixed-Norm Spaces: Full-Range Boundedness and Compactness",
  "title_text": "Fock Projections between Gaussian Mixed-Norm Spaces: Full-Range Boundedness and Compactness",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/58nfjazts0v8m",
  "venue": "arXiv",
  "versions": []
}