{
  "abstract": "In their seminal work, F. Ricci and E. M. Stein [Proc. Nat. Acad. Sci. USA 83, 1--3 (1986)] introduced the oscillatory singular integral \\[ T_Pf(x)=\\mathrm{p.v.}\\int_{\\mathbb{R}^n} e^{iP(x,y)}\\frac{Ω(x-y)}{|x-y|^n}f(y)\\,dy, \\] and S. Chanillo and M. Christ [Duke Math. J. 55, 141--155 (1987)] established its weak-type $(1,1)$ inequality for smooth $Ω$. For the rough variant, however, the weak-type $(1,1)$ inequality remained a long-standing open question. In the present paper, we settle this problem: specifically, we prove that the rough oscillatory singular integral is of weak type $(1,1)$ with $Ω\\in L\\log^+L(\\mathbb{S}^{n-1})$. Moreover, we establish weak-type $(1,1)$ bounds for the rough maximal oscillatory operator associated with $T_P$, a result of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02789",
  "author_total": 2,
  "authors": [
    {
      "name": "Yanping Chen"
    },
    {
      "name": "Zhengyang Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64vz2q39agdr4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02789",
  "fulltext_url": null,
  "id": "64vz2q39agdr4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02789",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220439976",
  "pdf_url": "https://arxiv.org/pdf/2610.02789",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64vz2q39agdr4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.02789",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02789"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak type $(1,1)$ bounds for rough oscillatory singular integrals",
  "title_text": "Weak type (1,1) bounds for rough oscillatory singular integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/64vz2q39agdr4",
  "venue": "arXiv",
  "versions": []
}