{
  "abstract": "Let $\\mathcal H_g f(z)=\\int_0^1 f(t)g'(tz),dt$, and let $2<p<\\infty$. Set $t=2p/(p-2)$ and $X_j=2^{-j/p'}Δ_j g'$, where $Δ_j$ is the hard dyadic Taylor projection. We prove that $\\mathcal H_g:H^p\\to H^p$ is bounded if and only if $h\\mapsto(X_jh)_{j\\geq0}$ is bounded from $H^t$ to $\\ell^t(H^2)$. The square of this embedding norm equals the norm of the positive column operator $b\\mapsto\\sum_j b_j|X_j|^2$ from $\\ell^{p/2}$ to $L^{p/2}$. Coordinate tails yield essential-norm estimates and an exact compactness criterion, while Hardy duality gives an equivalent paraproduct formulation. The criterion is quantitatively invariant under admissible analytic dyadic resolutions and defines a resolution-independent Calderón symbol space equal to the Hilbert-range multiplier space. We construct a bounded noncompact dense-frequency symbol outside the known blockwise sufficient class. We also prove an exact Poisson-atomic testing theorem: finite positive Poisson mixtures recover the full norm, but no fixed atom count suffices. Finally, aggregate probability densities give an intrinsic atomic-complexity formula and a finite-bandwidth testing bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01116",
  "author_total": 1,
  "authors": [
    {
      "name": "Yicen Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8gatchv523bfq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01116",
  "fulltext_url": null,
  "id": "8gatchv523bfq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01116",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7206154551",
  "pdf_url": "https://arxiv.org/pdf/2609.01116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8gatchv523bfq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Vector-Carleson, Calderón, and Poisson-Atomic Criteria for Generalized Hilbert Operators on $H^p$, $p>2$",
  "title_text": "Vector-Carleson, Calderón, and Poisson-Atomic Criteria for Generalized Hilbert Operators on H^p, p>2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8gatchv523bfq",
  "venue": "arXiv",
  "versions": []
}