{
  "abstract": "Bayart, Pellegrino, and Rueda obtained diagonal absolute summability exponents for continuous \\(m\\)-linear operators from \\((\\ell_1)^m\\) into \\(\\ell_p\\). Their optimality was known for \\(2\\le p\\le\\infty\\), whereas the case \\(1\\le p<2\\) remained open. We settle the latter case by means of finite Walsh test operators, and consequently obtain the optimal exponent for every \\(1\\le p\\le\\infty\\). The same argument, combined with the corresponding interpolation and embedding results, also yields optimal Kwapień-type statements for several related range spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29443",
  "author_total": 3,
  "authors": [
    {
      "name": "Luis Miguel Castaño-Marín"
    },
    {
      "name": "Geivison Ribeiro"
    },
    {
      "name": "Diana Serrano-Rodríguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2pm7hdfhhwya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29443",
  "fulltext_url": null,
  "id": "f2pm7hdfhhwya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29443",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7204864878",
  "pdf_url": "https://arxiv.org/pdf/2608.29443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2pm7hdfhhwya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2608.29443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Optimality in a Multilinear Extension of Kwapień's Theorem",
  "title_text": "Optimality in a Multilinear Extension of Kwapień's Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/f2pm7hdfhhwya",
  "venue": "arXiv",
  "versions": []
}