{
  "abstract": "We characterize compactly supported functions $f$ in Dunkl--BMO spaces as those that can be written as \\begin{equation*} f=g+\\widetilde{S}_{μ,\\mathcal{P}}, \\end{equation*} the sum of some bounded function $g$ and the generalized balayage $\\widetilde{S}_{μ,\\mathcal{P}}$ of a Carleson measure on $\\mathbb{R}^{N}\\times(0,\\infty)$ associated with the Dunkl--Poisson semigroup. As a direct application of this representation of Dunkl--BMO functions, we establish a new characterization of the Hardy space in the Dunkl setting via a principal value integral related to $\\widetilde{S}_{μ,\\mathcal{P}}$. Moreover, analogous conclusions hold for the Dunkl--heat semigroup as well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05092",
  "author_total": 1,
  "authors": [
    {
      "name": "Qingdong Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d0p0c9cf2xck.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05092",
  "fulltext_url": null,
  "id": "4d0p0c9cf2xck",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05092",
  "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"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220714716",
  "pdf_url": "https://arxiv.org/pdf/2610.05092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d0p0c9cf2xck.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.05092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application",
  "title_text": "Dunkl--BMO functions representable in terms of generalized balayage of Carleson measures and an application",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/4d0p0c9cf2xck",
  "venue": "arXiv",
  "versions": []
}