{
  "abstract": "We prove a weak $(1,1)$ estimate for the full Poisson Littlewood--Paley $g$-function on every complete Riemannian manifold without boundary, with an explicit universal constant approximately equal to $3.33606$. The estimate requires no curvature restriction, volume doubling, heat kernel bound, or stochastic completeness. The proof combines a precise Poisson maximal inequality with a convex entropy identity; local elliptic regularity identifies the extension to arbitrary real $L^1$ data. As an application, we obtain weak $(1,1)$ estimates for certain spectral multipliers represented by Poisson time derivatives with coefficients in $L^2((0,\\infty),dt/t)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21847",
  "author_total": 3,
  "authors": [
    {
      "name": "Bo Li"
    },
    {
      "name": "Ji Li"
    },
    {
      "name": "Jinxia Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mb4wsh005yr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21847",
  "fulltext_url": null,
  "id": "3mb4wsh005yr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21847",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222558277",
  "pdf_url": "https://arxiv.org/pdf/2610.21847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mb4wsh005yr6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A geometry-independent endpoint estimate for the Littlewood--Paley $g$-function generated by the Poisson semigroup",
  "title_text": "A geometry-independent endpoint estimate for the Littlewood--Paley g-function generated by the Poisson semigroup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/3mb4wsh005yr6",
  "venue": "arXiv",
  "versions": []
}