{
  "abstract": "We give a geometric proof of the radial Kunze--Stein phenomenon on the good vertices of a thick, locally finite, regular affine building of irreducible type. The proof uses a positive spherical function, its joint eigenvalues for sphere averages, and the growth of vector-distance spheres. Conjugation by this function and complex interpolation yield a weighted $\\ell^2$ estimate and the boundedness of radial operators with $\\ell^p$ kernels for $1\\leq p<2$. We also present proofs by the averaging operators norms, by the Schur test and by Helgason transform. A further interpolation gives weighted mixed-exponent estimates. No transitivity assumption on the automorphism group is required; in particular the argument applies to buildings of type $\\widetilde A_2$ without a Bruhat--Tits realization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07889",
  "author_total": 1,
  "authors": [
    {
      "name": "Łukasz Pawlak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1r33vwf2qb6ya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07889",
  "fulltext_url": null,
  "id": "1r33vwf2qb6ya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07889",
  "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.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1r33vwf2qb6ya.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Group-free radial Kunze-Stein phenomenon on affine buildings",
  "title_text": "Group-free radial Kunze-Stein phenomenon on affine buildings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/1r33vwf2qb6ya",
  "venue": "arXiv",
  "versions": []
}