{
  "abstract": "We introduce the non-symmetric heat and Poisson semigroups associated with the Heckman-Opdam Laplacian in the compact setting. Based on the Poisson semigroup, we study several Littlewood-Paley $g$-functions in the spirit of Stein's work for compact Lie groups and prove their $L^{p}$-boundedness for $1<p\\leq 2$ and for some of them also for $1<p<\\infty$. As an application, we define associated Riesz transforms and imaginary powers and prove their $L^{p}$-continuity for $1<p<\\infty$. Passing to the average with respect to the action of the associated reflection group, we obtain $L^{p}$-boundedness of $g$-functions for the symmetric Poisson semigroup for all $1<p<\\infty$. In particular, our framework covers the Littlewood-Paley-Stein theory for Jacobi polynomial expansions and corresponding direct product settings as special cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12722",
  "author_total": 2,
  "authors": [
    {
      "name": "Lukas Langen"
    },
    {
      "name": "Margit Rösler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dns4snyqts9g4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12722",
  "fulltext_url": null,
  "id": "dns4snyqts9g4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12722",
  "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.RT"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213020512",
  "pdf_url": "https://arxiv.org/pdf/2609.12722",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dns4snyqts9g4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.12722",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12722"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Littlewood-Paley theory for orthogonal expansions associated with root systems",
  "title_text": "Littlewood-Paley theory for orthogonal expansions associated with root systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/dns4snyqts9g4",
  "venue": "arXiv",
  "versions": []
}