{
  "abstract": "Let $G_m$ be a bounded Vilenkin group and put $R:=\\sup_j m_j$. We prove the sharp uniform estimate $$\\|K_n\\|_1\\leq \\frac{17}{15\\ln 2}\\ln R,\\qquad n\\geq1,$$ for the Fejér kernels associated with the Vilenkin system. The constant $17/(15\\ln2)$ is best possible. In the Walsh--Paley case $R=2$, the result reduces exactly to Toledo's sharp estimate $\\sup_n\\|K_n\\|_1=17/15$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.09929",
  "author_total": 2,
  "authors": [
    {
      "name": "Nika Areshidze"
    },
    {
      "name": "George Tephnadze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hqh3jny7r2ge.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.09929",
  "fulltext_url": null,
  "id": "2hqh3jny7r2ge",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.09929",
  "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.GM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.09929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hqh3jny7r2ge.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:33Z",
      "native_id": "2611.09929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.09929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Sharp Logarithmic Bounds for Vilenkin-Fejér Kernels",
  "title_text": "Sharp Logarithmic Bounds for Vilenkin-Fejér Kernels",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/2hqh3jny7r2ge",
  "venue": "arXiv",
  "versions": []
}