{
  "abstract": "In this paper, we establish the weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orthogonality of the kernels themselves in the pseudo-localization arguments for the good functions and use the microlocal decomposition and $TT^*$ arguments for the bad functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38671",
  "author_total": 1,
  "authors": [
    {
      "name": "Xudong Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bahsjhvxa06mm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38671",
  "fulltext_url": null,
  "id": "bahsjhvxa06mm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38671",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7215030267",
  "pdf_url": "https://arxiv.org/pdf/2609.38671",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bahsjhvxa06mm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38671",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38671"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels",
  "title_text": "Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/bahsjhvxa06mm",
  "venue": "arXiv",
  "versions": []
}