{
  "abstract": "Let \\(0<α\\leq1\\), and let \\(g_α\\) be the Littlewood-Paley function associated with the fractional Poisson kernel, which reduces to the classical \\(g\\)-function when \\(α=1\\). We establish dimension-free \\(L^p\\) bounds for \\(g_α\\) for every \\(1<p<\\infty\\) and identify its exact \\(L^2\\) norm as \\(\\sqrt{α/2}\\). We further determine the precise asymptotic behavior of the weak-type \\((1,1)\\) constant as \\(n\\to\\infty\\), yielding quantitative upper and lower bounds in terms of the dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32387",
  "author_total": 5,
  "authors": [
    {
      "name": "Hui Li"
    },
    {
      "name": "Ziyuan Lian"
    },
    {
      "name": "Honghai Liu"
    },
    {
      "name": "Zengyan Si"
    },
    {
      "name": "Jie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e47bv7n6fjer7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32387",
  "fulltext_url": null,
  "id": "e47bv7n6fjer7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32387",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214780960",
  "pdf_url": "https://arxiv.org/pdf/2609.32387",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e47bv7n6fjer7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32387",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32387"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On $L^p$ bounds for the Littlewood-Paley $g_α$ function with fractional poisson kernel",
  "title_text": "On L^p bounds for the Littlewood-Paley g_α function with fractional poisson kernel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/e47bv7n6fjer7",
  "venue": "arXiv",
  "versions": []
}