{
  "abstract": "The spherical maximal operator of order $μ$ was introduced by El Kohen in the setting of real hyperbolic spaces, where its $L^p$-boundedness properties were studied. In this paper, we extend this notion to rank-one Riemannian symmetric spaces of noncompact type. We establish sufficient conditions on the parameter $μ$ for the corresponding spherical maximal operator to be bounded on $L^p$ for $1<p\\leq\\infty$. We also obtain a necessary condition for $L^p$-boundedness when $μ$ is real and $1<p<\\infty$. In particular, for $1<p\\leq2$, the necessary condition agrees with the sufficient condition, yielding the sharp range of real $μ$ in this regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15514",
  "author_total": 2,
  "authors": [
    {
      "name": "Subir Dakshi"
    },
    {
      "name": "Sanjoy Pusti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ct1asptyez43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15514",
  "fulltext_url": null,
  "id": "4ct1asptyez43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15514",
  "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": "W7213225076",
  "pdf_url": "https://arxiv.org/pdf/2609.15514",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ct1asptyez43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15514",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15514"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type",
  "title_text": "Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4ct1asptyez43",
  "venue": "arXiv",
  "versions": []
}