{
  "abstract": "On the real hyperbolic space $\\mathbb{H}^n$, the classical Muckenhoupt condition does not describe the weights $w$ for which the Hardy-Littlewood maximal operator $M$ is bounded on $L^p(w)$. We show that, for $1<p<\\infty$, $M$ is bounded on $L^p(w)$ if and only if $w$ is a local $A_p$ weight and satisfies a two-layer condition, which compares $w$ and its dual weight on two layers of the shadow of a point. We also treat the weak type case, radial weights and the range $p\\le1$, and we prove a weighted Herz principle for radial convolution operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26818",
  "author_total": 1,
  "authors": [
    {
      "name": "Tapendu Rana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btzv3f5c467zk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26818",
  "fulltext_url": null,
  "id": "btzv3f5c467zk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26818",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222996289",
  "pdf_url": "https://arxiv.org/pdf/2610.26818",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btzv3f5c467zk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26818"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces",
  "title_text": "Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/btzv3f5c467zk",
  "venue": "arXiv",
  "versions": []
}