{
  "abstract": "Let $\\mathcal R$ be a normalized root system in $\\mathbb R^N$ with a nonnegative multiplicity function $k$, and let $\\mathcal F$ be the associated Dunkl transform. We prove a Hörmander multiplier theorem on the Hardy spaces $H^p_{\\mathrm{Dunkl}}$, $0<p\\le1$, defined by conical Littlewood--Paley square functions. Let $W_2^s$ denote the classical Sobolev space in $\\mathbb{R}^N$. More precisely, if a multiplier $m$ satisfies \\[ \\sup_{t>0} \\|ψ(\\cdot)m(t\\cdot)\\|_{W_2^s}<\\infty \\] for a nonzero radial cutoff $ψ\\in C_c^\\infty(\\mathbb R^N\\setminus\\{0\\})$ and \\[ s>\\mathbf N\\left(\\frac1p-\\frac12\\right), \\] where $\\mathbf N$ is the homogeneous dimension, then the Dunkl multiplier \\[ \\mathcal T_mf=\\mathcal F^{-1}(m\\mathcal Ff) \\] extends to a bounded operator on $H^p_{\\mathrm{Dunkl}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18621",
  "author_total": 2,
  "authors": [
    {
      "name": "Jacek Dziubański"
    },
    {
      "name": "Agnieszka Hejna-Łyżwa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f86r7kdaz5k5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18621",
  "fulltext_url": null,
  "id": "f86r7kdaz5k5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18621",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213527999",
  "pdf_url": "https://arxiv.org/pdf/2609.18621",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f86r7kdaz5k5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18621",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18621"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Remark on Hörmander Multipliers on Dunkl Hardy Spaces",
  "title_text": "A Remark on Hörmander Multipliers on Dunkl Hardy Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/f86r7kdaz5k5d",
  "venue": "arXiv",
  "versions": []
}