{
  "abstract": "In this paper, we study the spherical maximal operator $\\mathcal{M}_{S^{d-1}(A)}$, which is associated with the sphere $S^{d-1}$ embedded in the horizontal plane of some nilpotent group $\\mathbb{G}_A$. Here, $\\mathbb{G}_A$ is the group identified with $\\mathbb{R}^{d+1}$, and its group law is determined by the $d\\times d$ real matrix $A$. Specifically, when $A$ is a skew-symmetric matrix $J$, which is the case of the Heisenberg group, it was known that the spherical maximal operator $\\mathcal{M}_{S^{d-1}(J)}$ is bounded on $L^p(\\mathbb{G}_J)$ for $p$ in the range $(\\frac{d}{d-1},\\infty]$. In this paper, we extend the results from the skew-symmetric matrix $J$ to a more general class of invertible matrices $A$. We aim to classify the range of $p$ for which the operator $\\mathcal{M}_{S^{d-1}(A)}$ is bounded on $L^p(\\mathbb{G}_A)$ based on the eigenvalues of $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Studia Math (2025) 282(1) 25-26 Published at Studia Math 282(1) 25-67 2025",
  "arxiv": "2610.36828",
  "author_total": 1,
  "authors": [
    {
      "name": "Joonil Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c3nkft1qvtwp7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36828",
  "fulltext_url": null,
  "id": "c3nkft1qvtwp7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36828",
  "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/2610.36828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c3nkft1qvtwp7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spherical Averages on nilpotent Groups",
  "title_text": "Spherical Averages on nilpotent Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/c3nkft1qvtwp7",
  "venue": "arXiv",
  "versions": []
}