{
  "abstract": "We study the Dunkl--Schrödinger operator $L=-Δ_k+V$ on $\\mathbb R^N$, $N>2$, where $V$ is a nonnegative potential in the reverse Hölder class ${\\rm RH}^q(dw)$, $q>\\mathbf N/2$, and $\\mathbf N$ is the homogeneous dimension. We establish decay estimates for the resolvent kernel in terms of the critical radius and the orbit distance. For reflection-invariant potentials, we obtain $L^p(dw)$ bounds for $VL^{-1}$, second-order Dunkl derivatives of $L^{-1}$, and the Riesz transform $\\nabla_kL^{-1/2}$, together with fractional potential and mixed estimates. The proofs combine local estimates for weak solutions, the Dunkl Fefferman--Phong inequality, and kernel estimates adapted to the Euclidean and orbit distances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08371",
  "author_total": 2,
  "authors": [
    {
      "name": "Agnieszka Hejna-Łyżwa"
    },
    {
      "name": "Suman Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8akwzqqgnb4y3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08371",
  "fulltext_url": null,
  "id": "8akwzqqgnb4y3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08371",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220960220",
  "pdf_url": "https://arxiv.org/pdf/2610.08371",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8akwzqqgnb4y3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08371",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08371"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^p$ estimates for Dunkl--Schrödinger operators",
  "title_text": "L^p estimates for Dunkl--Schrödinger operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/8akwzqqgnb4y3",
  "venue": "arXiv",
  "versions": []
}