{
  "abstract": "We show that the strong maximal operator on ${\\mathbb R}^2$ does not satisfy a linear weighted $L^2$ estimate in terms of the rectangular $A_2$ characteristic. More precisely, we construct weights with arbitrarily large characteristic for which the operator norm is bounded below by $[w]_{A_2^{\\mathrm{str}}}\\sqrt{\\log [w]_{A_2^{\\mathrm{str}}}}$. The proof is elementary. It uses an explicit two-parameter mass recurrence on a product of geometric interval partitions, together with a direct comparison of arbitrary rectangular averages with anchored averages.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14008",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrei K. Lerner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a0113qcvwectx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14008",
  "fulltext_url": null,
  "id": "a0113qcvwectx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14008",
  "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": "W7213252301",
  "pdf_url": "https://arxiv.org/pdf/2609.14008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a0113qcvwectx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14008"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of the linear $A_2$ bound for the strong maximal operator",
  "title_text": "Failure of the linear A_2 bound for the strong maximal operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/a0113qcvwectx",
  "venue": "arXiv",
  "versions": []
}