{
  "abstract": "Let $M=\\mathbb R^m\\sharp(\\mathbb R^n\\times\\mathbb S^{m-n})$, where $m>n\\geq3$. The full-cone Poisson area and non-tangential maximal functions fail to be of weak type $(p,p)$ for $1<p<2$. Let $K$ be the compact part joining the two ends and put $ρ(x)=1+d(x,K)$. For fixed small $c>0$, we restrict the horizontal distance from the vertex to $cρ(x)$ and retain every positive time. The resulting maximal function is of weak type $(1,1)$ and bounded on $L^p$ for $1<p\\leq\\infty$. The corresponding area function uses the full spatial and time gradient. It satisfies a Fefferman--Stein distribution inequality. Its $L^p$ norm is equivalent to that of $f$ for $1<p\\leq2$. This area function defines a global Hardy space. We prove its $Δ$-atomic description, its injective embedding into $L^1$, its characterization by the restricted maximal function, and its real interpolation identity with $L^2$. Direct estimates for spectral-band kernels then give a Mihlin multiplier theorem from this Hardy space to $L^1$. Interpolation and duality give $L^p$ boundedness for every $1<p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04177",
  "author_total": 3,
  "authors": [
    {
      "name": "Peng Chen"
    },
    {
      "name": "Ji Li"
    },
    {
      "name": "Lixin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bvm3sxj37epz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04177",
  "fulltext_url": null,
  "id": "4bvm3sxj37epz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04177",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bvm3sxj37epz.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Poisson area and non-tangential maximal functions on manifolds with ends and applications",
  "title_text": "Poisson area and non-tangential maximal functions on manifolds with ends and applications",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/4bvm3sxj37epz",
  "venue": "arXiv",
  "versions": []
}