{
  "abstract": "Let $Δ_k$ be the Dunkl Laplacian associated with an arbitrary root system and a nonnegative multiplicity function. For every $0<p\\leq1$, a Coifman-Weiss type atomic characterization of the Hardy space $H^p_{\\mathrm{Dunkl}}$ is established. More precisely, it is proved that the space $H^p_{\\mathrm{Dunkl}}$, which is originally defined by a relevant square function, coincides with the space generated by $({\\rm CW},p,2)$-atoms, that is, atoms supported on Euclidean balls and satisfying cancellation conditions against all polynomials of degree $ \\leq s_p$, where \\[ s_p=\\left\\lfloor \\mathbf N\\left(\\frac1p-1\\right)\\right\\rfloor \\] and $\\mathbf N$ is the homogeneous dimension of the underlying Dunkl measure. The corresponding quasi-norms are equivalent. We also show that the same space is obtained when the $L^2$ size condition in the definition of atoms is replaced by the $L^\\infty$ size condition. The strategy of the proof is to use an operator-type atomic decomposition associated with the Dunkl Laplacian, and then prove that each such operator atom can be written a linear combination of $({\\rm CW},p,2)$-atoms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17070",
  "author_total": 2,
  "authors": [
    {
      "name": "Jacek Dziubański"
    },
    {
      "name": "Agnieszka Hejna-Łyżwa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q40xwpnescwk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17070",
  "fulltext_url": null,
  "id": "7q40xwpnescwk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17070",
  "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": "W7213406556",
  "pdf_url": "https://arxiv.org/pdf/2609.17070",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q40xwpnescwk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.17070",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17070"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$H^p$ spaces in the Dunkl setting meet Coifman--Weiss--type atoms",
  "title_text": "H^p spaces in the Dunkl setting meet Coifman--Weiss--type atoms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7q40xwpnescwk",
  "venue": "arXiv",
  "versions": []
}