{
  "abstract": "Let $d\\ge3$ and $2\\le r<\\infty$. We consider the strong maximal operator associated with Euclidean surface averages over the $\\ell^r$ unit sphere and independent coordinate dilations. We prove that this operator is bounded on $L^p(\\mathbb R^d)$ if and only if \\[ p>\\max\\left\\{\\frac{d+1}{d-1},\\frac{r}{d-1}\\right\\}. \\] We also obtain $L^p\\to L^q$ bounds for the corresponding local maximal operator. For each fixed $p$ in certain ranges, the resulting range of $q$ is optimal up to endpoints. The proof uses a dyadic surface decomposition and frequency-localized $L^2$ estimates. We establish these estimates by combining exact multiplier factorization via iterated stationary phase with scalar Fourier inversion and $TT^*$ arguments. In dimension three, these estimates are combined with quantitative multiparameter local smoothing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04968",
  "author_total": 3,
  "authors": [
    {
      "name": "Jin Bong Lee"
    },
    {
      "name": "Sanghyuk Lee"
    },
    {
      "name": "Jeongtae Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7560k4qs4fb61.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04968",
  "fulltext_url": null,
  "id": "7560k4qs4fb61",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04968",
  "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": "W7220651156",
  "pdf_url": "https://arxiv.org/pdf/2610.04968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7560k4qs4fb61.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The strong $\\ell^r$ spherical maximal function",
  "title_text": "The strong ℓ^r spherical maximal function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7560k4qs4fb61",
  "venue": "arXiv",
  "versions": []
}