{
  "abstract": "Let $μ$ be a doubling Radon measure in $\\mathbb R^d$ with support $X$. We prove a local and quantitative form of the Bennewitz--Lewis theorem in this setting: if a Radon measure $ν$ satisfies the Bennewitz--Lewis condition on a bounded relatively open set $V\\subset X$ with a small enough constant, then $ν|_V\\llμ|_V$ and its density satisfies a reverse Hölder inequality on every compact subset $K\\subset V$. Along the way we develop the dyadic toolkit these arguments run on --- triple cubes defined through neighbours, the basis $\\mathcal{D}\\cup3\\mathcal{D}$, and a Whitney decomposition --- and we collect the Muckenhoupt-type classes of weights over that basis. The same machinery yields a local Gehring lemma for enlarged balls: both theorems are deduced from a single bootstrapping lemma, stated once for $p=1$ and $p>1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05320",
  "author_total": 1,
  "authors": [
    {
      "name": "Martí Prats"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dben29demgk3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05320",
  "fulltext_url": null,
  "id": "4dben29demgk3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05320",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220704036",
  "pdf_url": "https://arxiv.org/pdf/2610.05320",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dben29demgk3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05320",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05320"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak reverse Hölder inequalities for doubling measures",
  "title_text": "Weak reverse Hölder inequalities for doubling measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4dben29demgk3",
  "venue": "arXiv",
  "versions": []
}