{
  "abstract": "We disprove the cap-sufficiency proposal in Wright's Problem 16 for $1<p<(\\sqrt{13}-1)/2$ and for $p>3$. For each fixed exponent in these ranges, one smooth strictly convex domain has finite original directional cap integral, while the lacunary maximal operator of complete arclength fails restricted weak type. We also give a geometric sufficient condition for strong $L^p$ boundedness, for every finite $1<p<\\infty$, on an arbitrary given bounded convex domain. It requires one logarithmic integral of a curvature lower envelope, without a differentiability assumption on the boundary or a restriction on the number of curvature zeros. Both results concern unnormalised true arclength, one fixed interior origin and all integer dyadic dilations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32873",
  "author_total": 2,
  "authors": [
    {
      "name": "Xi Cen"
    },
    {
      "name": "Xinfeng Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29ns8dypepk4j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32873",
  "fulltext_url": null,
  "id": "29ns8dypepk4j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32873",
  "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": "W7223675780",
  "pdf_url": "https://arxiv.org/pdf/2610.32873",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29ns8dypepk4j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32873",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32873"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lacunary maximal operators on convex boundaries",
  "title_text": "Lacunary maximal operators on convex boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/29ns8dypepk4j",
  "venue": "arXiv",
  "versions": []
}