{
  "abstract": "The primary objective of this paper is to establish the pointwise almost everywhere convergence of the singular integrals of Christ-Journé type. To this end, we prove the weak type $(1,1)$ estimate for the corresponding maximal operator defined as \\[ T^*[a] f(x):= \\sup_{r>0}\\left|\\int_{|x-y| > r} K(x-y) \\int_0^1 a(tx + (1-t)y)\\, dt f(y)\\, dy\\right|, \\] where $K$ is a Calderón--Zygmund kernel and $a\\in L^\\infty$. This result resolves a problem posed by Seeger (Rev. Mat. Iberoam., 2014).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04673",
  "author_total": 3,
  "authors": [
    {
      "name": "Ankit Bhojak"
    },
    {
      "name": "Sangita Kundu"
    },
    {
      "name": "Saurabh Shrivastava"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ebqprtq7xbs0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04673",
  "fulltext_url": null,
  "id": "8ebqprtq7xbs0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04673",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220705624",
  "pdf_url": "https://arxiv.org/pdf/2610.04673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ebqprtq7xbs0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04673"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On pointwise convergence of singular integrals of Christ-Journé type",
  "title_text": "On pointwise convergence of singular integrals of Christ-Journé type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8ebqprtq7xbs0",
  "venue": "arXiv",
  "versions": []
}