{
  "abstract": "Let $p\\in[1,\\infty)$ and $δ\\in(0,n]$. Recently, to characterize the weighted boundedness of maximal operator on Choquet integrals based on Hausdorff content $\\mathcal H_\\infty^δ$, a class of Capacity Muckenhoupt weights is introduced, denoted by $\\mathcal A_{p,δ}$, and, for any fixed $δ\\in(0,n]$, this new class of weights is proved to satisfy the self-improving property with respect to the index $p\\in(1,\\infty)$. In this note, we show that, for every fixed $p\\in[1,\\infty)$, the class of capacity Muckenhoupt weights $\\mathcal A_{p,δ}$ fails to satisfy the self-improving property with respect to the index $δ\\in(0,n]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39313",
  "author_total": 2,
  "authors": [
    {
      "name": "Yangzhi Zhang"
    },
    {
      "name": "Ciqiang Zhuo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2zh63bmp99j4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39313",
  "fulltext_url": null,
  "id": "d2zh63bmp99j4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39313",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7215129349",
  "pdf_url": "https://arxiv.org/pdf/2609.39313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2zh63bmp99j4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Note on Capacity Muckenhoupt Weights with respect to the Hausdorff Content",
  "title_text": "A Note on Capacity Muckenhoupt Weights with respect to the Hausdorff Content",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/d2zh63bmp99j4",
  "venue": "arXiv",
  "versions": []
}