{
  "abstract": "We prove that the Bohnenblust--Hille constants for Walsh polynomials on the Hamming cube grow at most polynomially in the degree. More precisely, there is an absolute constant $K$ such that every $f :\\{-1,1\\}^{n} \\to \\mathbb{C}$ of degree at most $m$ satisfies $$ \\left(\\sum_{|S|\\le m}|\\widehat f(S)|^{2m/(m+1)}\\right)^{(m+1)/(2m)} \\le Km^{27}\\|f\\|_\\infty. $$ The estimate is uniform in the dimension. The exponent $27$ is not optimized.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12427",
  "author_total": 1,
  "authors": [
    {
      "name": "Paata Ivanisvili"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/favn9jqjy4ees.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12427",
  "fulltext_url": null,
  "id": "favn9jqjy4ees",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12427",
  "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.CO"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7212584868",
  "pdf_url": "https://arxiv.org/pdf/2609.12427",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/favn9jqjy4ees.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12427",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12427"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Polynomial growth of Bohnenblust--Hille constants on the Hamming cube",
  "title_text": "Polynomial growth of Bohnenblust--Hille constants on the Hamming cube",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/favn9jqjy4ees",
  "venue": "arXiv",
  "versions": []
}