{
  "abstract": "Let $M_t$ denote the normalized average over the lattice points in the Euclidean ball of radius $t$ in $\\mathbb{Z}^d$. We prove that the full maximal operator $f\\mapsto\\sup_{t\\geq0}\\lvert M_t f\\rvert$ is bounded on $\\ell^p(\\mathbb{Z}^d)$, for every $1<p\\leq\\infty$, with a constant independent of the dimension. In particular, this resolves a question of E.M. Stein from the mid 1990s. The principal ingredient in our proof is that, when $t\\lesssim d$ with $t$ sufficiently large, the associated multiplier $\\mathfrak{m}_{\\sqrt{\\lfloor t^2\\rfloor}}(ξ)$ admits an asymptotic expansion of arbitrary prescribed order, uniform in $ξ$, whose resulting maximal operators can be controlled by the discrete normalized Gaussian maximal function studied by Mirek--Szarek--Wróbel \\cite{MSW25}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10083",
  "author_total": 1,
  "authors": [
    {
      "name": "Sheng-Chen Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7akg7j5269qth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10083",
  "fulltext_url": null,
  "id": "7akg7j5269qth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10083",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212125149",
  "pdf_url": "https://arxiv.org/pdf/2609.10083",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7akg7j5269qth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.10083",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10083"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dimension-free estimates for the full discrete Euclidean ball maximal function",
  "title_text": "Dimension-free estimates for the full discrete Euclidean ball maximal function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/7akg7j5269qth",
  "venue": "arXiv",
  "versions": []
}