{
  "abstract": "Let 1 < rho < n and let Omega be in Lrho(S^(n-1)) with vanishing mean. We prove that the maximal truncation T*_Omega of the rough singular integral T_Omega is pointwise dominated by finitely many sparse potentials of the form: sum over Q in S of l(Q) * ( (1/|Q|) * integral over Q of |nabla f|^p )^(1/p), where 1/rho~ = 1/rho' + 1/n and rho~ <= p < n. This estimate is uniform in the truncation parameter and extends the subcritical bound of Hoang, Moen, and Perez for T_Omega to T*_Omega. Since the argument does not require the boundedness of T*_Omega on the target space, it yields two-weight Sobolev inequalities: norm(T*_Omega f, L^q(u)) <= C * norm(nabla f, L^p(v)), under joint two-weight conditions, while the target weight u itself is only required to belong to A_infinity. Additionally, we prove a Hedberg-type estimate involving a Morrey norm of the gradient and apply it to weighted grand Lebesgue spaces. Further consequences are obtained in weighted Lebesgue, Orlicz, and variable Lebesgue spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19185",
  "author_total": 3,
  "authors": [
    {
      "name": "Diego Chamorro"
    },
    {
      "name": "Anca-Nicoleta Marcoci"
    },
    {
      "name": "Liviu-Gabriel Marcoci"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drahj0f69hy5r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19185",
  "fulltext_url": null,
  "id": "drahj0f69hy5r",
  "issns": [],
  "landing_url": "https://hal.science/hal-05746501v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
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  "openalex": "W7213476588",
  "pdf_url": "https://hal.science/hal-05746501/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drahj0f69hy5r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:33Z",
      "native_id": "hal-05746501",
      "source": "hal",
      "url": "https://hal.science/hal-05746501v1"
    },
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19185",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19185"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "SPARSE POINTWISE BOUNDS FOR MAXIMAL TRUNCATIONS OF ROUGH SINGULAR INTEGRALS AND SOBOLEV-TYPE INEQUALITIES",
  "title_text": "SPARSE POINTWISE BOUNDS FOR MAXIMAL TRUNCATIONS OF ROUGH SINGULAR INTEGRALS AND SOBOLEV-TYPE INEQUALITIES",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/drahj0f69hy5r",
  "venue": "HAL",
  "versions": []
}