{
  "abstract": "In this paper, we establish a noncommutative version of Andreas Seeger's weak type $(1,1)$ estimate for singular integral operators with kernels satisfying angular $L\\log L$ integrability and an averaged radial Dini condition. The strategy for obtaining the sharp integrability condition involves not only some new estimates of the off-diagonal good and bad functions in Parcet's noncommutative Calderón-Zygmund decomposition but also certain essential modifications of Seeger's kernel decomposition and estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25339",
  "author_total": 4,
  "authors": [
    {
      "name": "Guixiang Hong"
    },
    {
      "name": "Liang Wang"
    },
    {
      "name": "Xumin Wang"
    },
    {
      "name": "Bang Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ckgf057fgmgn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25339",
  "fulltext_url": null,
  "id": "1ckgf057fgmgn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25339",
  "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.OA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223050939",
  "pdf_url": "https://arxiv.org/pdf/2610.25339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ckgf057fgmgn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A noncommutative weak $L_1$-estimate for rough singular integrals",
  "title_text": "A noncommutative weak L_1-estimate for rough singular integrals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1ckgf057fgmgn",
  "venue": "arXiv",
  "versions": []
}