{
  "abstract": "The polynomial Hardy--Littlewood inequalities bound coefficient norms of homogeneous polynomials on $\\ell_p$ balls by their supremum norms, with constants independent of the dimension. Their $p=\\infty$ endpoint is the Bohnenblust--Hille inequality. A longstanding obstruction to connecting their constants is the polarization loss in the usual multilinear approach. We overcome this obstruction by proving $D_{m,p_m}\\le(1+o(1))D_m$ whenever $p_m/m^2\\to\\infty$, where $D_{m,p}$ and $D_m$ are the optimal complex polynomial Hardy--Littlewood and Bohnenblust--Hille constants. At the opposite boundary, we determine the optimal endpoint constant exactly, $D_{m,m}=m$. We then prove the full first-order asymptotic $D_{m,p_m}\\sim m$ whenever $p_m\\ge m$ and $p_m-m\\to0$, and the exact polynomial growth $D_{m,p_m}=m^{1+o(1)}$ on the wider scale $p_m-m=o((m/\\log m)^{1/3})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14909",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel Pellegrino"
    },
    {
      "name": "Eduardo Teixeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vqdracsrsh6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14909",
  "fulltext_url": null,
  "id": "2vqdracsrsh6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14909",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213288108",
  "pdf_url": "https://arxiv.org/pdf/2609.14909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vqdracsrsh6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.14909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hardy--Littlewood Constants Beyond Polarization",
  "title_text": "Hardy--Littlewood Constants Beyond Polarization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2vqdracsrsh6s",
  "venue": "arXiv",
  "versions": []
}