{
  "abstract": "In 1997, Belinsky conjectured that, for convex subsequences, the logarithmic growth condition of Carleson, Trigub, and Zagorodni\\uı is necessary and sufficient for the arithmetic means of subsequential Fourier partial sums to converge at every Lebesgue point of every integrable function. We disprove the sufficiency part of this conjecture. More precisely, we construct a strictly convex increasing sequence $(a_m)$ satisfying $a_m\\leq 7m^8$ and a function $f\\in L^1(\\mathbb T)$ for which $0$ is a Lebesgue point, $f(0)=0$, and the means $m^{-1}\\sum_{k=1}^m S_{a_k}f(0)$ are unbounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30575",
  "author_total": 1,
  "authors": [
    {
      "name": "Ushangi Goginava"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91fj2957g2b48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30575",
  "fulltext_url": null,
  "id": "91fj2957g2b48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30575",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W7204927709",
  "pdf_url": "https://arxiv.org/pdf/2608.30575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91fj2957g2b48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Counterexample to Belinsky's Conjecture on Cesàro Means at Lebesgue Points",
  "title_text": "A Counterexample to Belinsky's Conjecture on Cesàro Means at Lebesgue Points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/91fj2957g2b48",
  "venue": "arXiv",
  "versions": []
}