{
  "abstract": "Let $R\\subset\\mathbb{R}^d$ be a reduced root system, $G$ the associated finite reflection group, and $k\\ge0$ a $G$-invariant multiplicity function. We develop a Dunkl analogue of the obstacle/partial-balayage method of Ouyang, Spector, and Stockdale (https://arxiv.org/abs/2608.18068) for the Euclidean fractional Laplacian. For $0<s<2$, nonnegative $f\\in L^1(ν_k)\\cap L^2(ν_k)$, and $λ>0$, we obtain a decomposition \\[ f=μ+(-Δ_k)^{s/2}u, \\qquad 0\\leμ\\leλ, \\] with $μ=λ$ on $Ω=\\{u>0\\}$ and \\[ λν_k(Ω)\\le\\|f\\|_{L^1(ν_k)}. \\] As an application, we prove that the vector Dunkl--Riesz transform $\\mathcal R_k=\\nabla_k(-Δ_k)^{-1/2}$ is of weak type $(1,1)$ with constant at most $(M_k+2)$, where \\[ M_k=\\#\\{α\\in R_+:k(α)>0\\}. \\] For $G$-invariant functions, the reflection terms vanish and the same argument gives the universal constant $2$. We further establish a dimension-free weak-type $(1,1)$ estimate for the Dunkl--Schrödinger Riesz transform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08492",
  "author_total": 1,
  "authors": [
    {
      "name": "Suman Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c39b45ab19e6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08492",
  "fulltext_url": null,
  "id": "6c39b45ab19e6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08492",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212000651",
  "pdf_url": "https://arxiv.org/pdf/2609.08492",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c39b45ab19e6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08492",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08492"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dimension free weak-type endpoint estimates for the vectors of the Dunkl--Riesz transform",
  "title_text": "Dimension free weak-type endpoint estimates for the vectors of the Dunkl--Riesz transform",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6c39b45ab19e6",
  "venue": "arXiv",
  "versions": []
}