{
  "abstract": "We establish sharp $L^p$ maximal estimates for averages over smooth nondegenerate curves in $\\mathbb R^n$ for $p>n$. More precisely, we show that for any nondegenerate curve $γ$ in $\\mathbb R^n$ and the associated maximal operator \\begin{equation} M f(x):=\\sup_{t>0} \\Big|\\int_{-1}^1f(x-tγ(s))χ(s)\\,\\mathrm{d}s\\Big|, \\end{equation} the estimate \\begin{equation} \\| Mf\\|_{L^p(\\mathbb R^n)}\\lesssim_{γ,p,n} \\|f\\|_{L^p(\\mathbb R^n)} \\end{equation} holds for all $p>n$. A new ingredient is a weighted Kakeya-type estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37250",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengwen Gan"
    },
    {
      "name": "Changkeun Oh"
    },
    {
      "name": "Jaehoon Shin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dxaxrywxsn9b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37250",
  "fulltext_url": null,
  "id": "4dxaxrywxsn9b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37250",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7224128104",
  "pdf_url": "https://arxiv.org/pdf/2610.37250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dxaxrywxsn9b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp helical maximal estimates in all dimensions",
  "title_text": "Sharp helical maximal estimates in all dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/4dxaxrywxsn9b",
  "venue": "arXiv",
  "versions": []
}