{
  "abstract": "In this paper we study the boundedness properties of a \\emph{hybrid} trilinear Hilbert transform characterized by a \\emph{dual regime} which simultaneously exhibits 1) \\emph{resonant} (zero curvature) features, \\emph{i.e.}, modulation invariance properties, and 2) \\emph{non-resonant} (non-zero curvature) features. Specifically, given $a\\in(0,\\infty)\\setminus \\{1,2\\}$ and $\\vecλ:=(λ_1,λ_2,λ_3,λ_4)\\in (\\mathbb{R}\\setminus\\{0\\})^4$ with $λ_1\\neq λ_2$ and $λ_3\\neq λ_4$, we provide wide-range $L^p$ bounds for the trilinear operator $$ HTHT^a_{\\vecλ} (f_1,f_2,f_3)(x):= p.v. \\int_{\\mathbb R} f_1(x-λ_1 t)\\,f_2(x-λ_2 t-λ_3 t^a)\\,f_3(x-λ_4 t^a)\\,\\frac{dt}{t},\\quad x \\in \\mathbb{R}\\,.$$ By combining variable multiresolution, multiscale wave-packet analysis, and Rank II LGC method, our present work establishes a common framework where the diverse methodologies of all of the following naturally converge: i) the maximal truncated bilinear Hilbert transform, ii) the Biest operator, iii) the hybrid bilinear Hilbert-Carleson operator, and iv) the non-resonant (curved) trilinear Hilbert transform. Ultimately, this work reveals that the hybrid trilinear transform sits on a critical intermediate scale between the purely non-resonant case and the purely resonant regime -- the latter remaining a challenging, major (open) problem in harmonic analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02167",
  "author_total": 3,
  "authors": [
    {
      "name": "Cristina Benea"
    },
    {
      "name": "Frédéric Bernicot"
    },
    {
      "name": "Victor Lie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7t1y0nxs6vq0t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02167",
  "fulltext_url": null,
  "id": "7t1y0nxs6vq0t",
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  "landing_url": "https://arxiv.org/abs/2611.02167",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7t1y0nxs6vq0t.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On a hybrid trilinear Hilbert transform",
  "title_text": "On a hybrid trilinear Hilbert transform",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7t1y0nxs6vq0t",
  "venue": "arXiv",
  "versions": []
}