{
  "abstract": "We study the optimal Bohnenblust-Hille constants $ K_{ m , M } $ for complex $ m $-homogeneous polynomials in any number of variables whose monomials with nonzero coefficient involve at most $M$ variables. For every fixed $M$, we prove that these constants satisfy \\[ K_{ m , M } \\leq A_{ M }^{ M / m } \\cdot m^{ ( M^2 - 1 ) / ( 2m ) } \\, , \\quad \\text{for} \\ m \\geq M \\, , \\] where $ A_{ M } \\geq 1 $ depends only on $ M $. In particular, \\[ K_{ m , M } \\to 1 \\quad \\text{as} \\ m \\to \\infty \\, , \\] and so the corresponding Bohnenblust-Hille constants are asymptotically contractive. The proof exploits the homogeneous structure through a decomposition according to exact monomial-support levels, partitions of the set of variables, multilinear Bohnenblust-Hille estimates, and interpolation with Parseval's identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20847",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicolás Caro-Montoya"
    },
    {
      "name": "Daniel Núñez-Alarcón"
    },
    {
      "name": "Diana Serrano-Rodríguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ta8vtbfxy8sz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20847",
  "fulltext_url": null,
  "id": "3ta8vtbfxy8sz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20847",
  "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.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.20847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ta8vtbfxy8sz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2607.20847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support",
  "title_text": "Asymptotic Contractivity of Bohnenblust-Hille Constants with Bounded Monomial Support",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/3ta8vtbfxy8sz",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s00574-026-00527-1",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}