{
  "abstract": "We establish sparse bounds for the trilinear Hilbert transform $$ T(f_1,f_2,f_3)(x):=\\textrm{p.v.}\\int_{\\mathbb R} f_1(x-t)f_2(x-2t)f_3(x-3t)\\,\\frac{dt}{t}, $$ with averaging exponents arbitrarily close to $2$ from above. As a consequence, we extend OpenAI's $L^3\\times L^3\\times L^3\\to L^1$ bound (entry 086 in the OpenAI Research Catalog) to $L^{p_1}\\times L^{p_2}\\times L^{p_3}\\to L^r$ throughout the range $$ 2<p_1,p_2,p_3<\\infty, \\qquad \\frac1r=\\frac1{p_1}+\\frac1{p_2}+\\frac1{p_3}, \\qquad \\frac23<r<2, $$ and obtain corresponding weighted estimates for weights in multilinear Muckenhoupt classes. Our proof relies on the normalized local estimate and stopping time argument developed in OpenAI's work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39096",
  "author_total": 1,
  "authors": [
    {
      "name": "Bingyang Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98x0518v6fh7k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39096",
  "fulltext_url": null,
  "id": "98x0518v6fh7k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39096",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98x0518v6fh7k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39096"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sparse domination and an extended $L^p$ range for the trilinear Hilbert transform",
  "title_text": "Sparse domination and an extended L^p range for the trilinear Hilbert transform",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/98x0518v6fh7k",
  "venue": "arXiv",
  "versions": []
}