{
  "abstract": "Building on the work of A. Córdoba and R. Fefferman, we provide a necessary and sufficient covering condition on a basis $\\mathcal{B}$ on a separable metric space $X$ with a Borel measure $μ$ so that the associated \\mbox{geometric} maximal operator $M_\\mathcal{B}$ satisfies for all $α> 0$ the weak type estimate $$μ\\left(\\left\\{x \\in X : M_\\mathcal{B}f(x) > α\\right\\}\\right) \\leq \\int_{X}Φ\\left( γ_\\mathcal{B} \\left|\\frac{f}α\\right|\\right)\\,dμ\\;,$$ where $Φ: [0, \\infty) \\rightarrow [0, \\infty)$ is an everywhere finite Young's function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30327",
  "author_total": 3,
  "authors": [
    {
      "name": "Paul Hagelstein"
    },
    {
      "name": "Fedor Nazarov"
    },
    {
      "name": "Blanca Radillo-Murguia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5b7ydrxhd6q9v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30327",
  "fulltext_url": null,
  "id": "5b7ydrxhd6q9v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30327",
  "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"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223403204",
  "pdf_url": "https://arxiv.org/pdf/2610.30327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5b7ydrxhd6q9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Covering lemmas associated to maximal operators of weak type",
  "title_text": "Covering lemmas associated to maximal operators of weak type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/5b7ydrxhd6q9v",
  "venue": "arXiv",
  "versions": []
}