{
  "abstract": "Let $M_ψ$ be the maximal operator associated to $ψ(x)=-\\ln(1-|x|^2)$. We obtain dimension-free bounds on $L^p(\\mathbb R^d)$ for $M_ψ$, $1<p\\le\\infty$. We show that the weak $L^1$ estimate does not hold for $M_ψ$, but does hold for the corresponding lacunary maximal operator $M_ψ^D$. An weak $L\\log L$ type estimate for $M_ψ$ is obtained, which seems to be the right substitution for the weak $L^1$ estimate. Estimates for $M_ψ$ are applied to dimension-free estimates for maximal Riesz transforms obtained by Mateu, Verdera, Orobitg and Pérez.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32641",
  "author_total": 4,
  "authors": [
    {
      "name": "Mingming Cao"
    },
    {
      "name": "Honghai Liu"
    },
    {
      "name": "Zengyan Si"
    },
    {
      "name": "Haibin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brt4a7xw3b2ap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32641",
  "fulltext_url": null,
  "id": "brt4a7xw3b2ap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32641",
  "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": "W7223706862",
  "pdf_url": "https://arxiv.org/pdf/2610.32641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brt4a7xw3b2ap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dimension-free bounds for maximal operators associated to log kernel and applications",
  "title_text": "Dimension-free bounds for maximal operators associated to log kernel and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/brt4a7xw3b2ap",
  "venue": "arXiv",
  "versions": []
}