{
  "abstract": "We prove convex body sparse bounds for coordinatewise Hilbert transforms along monomial curves and local $C^d$ curves with uniformly nonvanishing torsion on the closed integration interval. Adapting the scalar estimates of Cladek--Ou \\cite{CladekOu2018} and the lifting method of Laukkarinen--Lorist \\cite{LaukkarinenLorist2026} to the anisotropic geometry, we obtain one sparse family of genuine curve-adapted boxes and quantitative $L^p(W)$ bounds for matrix weights. The convex body sparse exponent range is sharp up to its boundary: estimates hold in the interior of $Ω_d$, while any fixed finite number of sparse families fails outside $\\overline{Ω_d}$ when $1/r+1/s>1$. We also establish an explicit endpoint-contact obstruction. For every interior planar exponent pair, a polynomial curve with positive torsion on the open integration interval violates the full-interval sparse estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40820",
  "author_total": 1,
  "authors": [
    {
      "name": "Xi Cen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8s7y5yyffq67e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40820",
  "fulltext_url": null,
  "id": "8s7y5yyffq67e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40820",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8s7y5yyffq67e.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp convex body sparse bounds and quantitative matrix weighted estimates for Hilbert transforms along curves",
  "title_text": "Sharp convex body sparse bounds and quantitative matrix weighted estimates for Hilbert transforms along curves",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/8s7y5yyffq67e",
  "venue": "arXiv",
  "versions": []
}