{
  "abstract": "Let $L=-Δ_k+V$ be a Schrödinger operator associated with the Dunkl Laplacian and a nonnegative potential. We characterize the Hardy space $H_L^1$, defined by the maximal operator of the semigroup generated by $-L$, in terms of the Riesz transforms associated with $L$. Under a local integral condition on the potential and a decay condition on the semigroup, formulated relative to an admissible covering by cubes, we prove that \\[ \\|f\\|_{H_L^1} \\asymp \\|f\\|_{L^1(dw)} +\\sum_{j=1}^N \\|\\widetilde{R}_j f\\|_{L^1(dw)}. \\] The proof combines an atomic characterization of $H_L^1$ with local Hardy space theory and weighted integral estimates for Dunkl derivatives of the heat kernels. The result applies to arbitrary root systems and nonnegative multiplicity functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00703",
  "author_total": 1,
  "authors": [
    {
      "name": "Agnieszka Hejna-Łyżwa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dnfzr30ehyagn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00703",
  "fulltext_url": null,
  "id": "dnfzr30ehyagn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00703",
  "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": "W7216122348",
  "pdf_url": "https://arxiv.org/pdf/2610.00703",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dnfzr30ehyagn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00703",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00703"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Riesz transform characterization of Hardy spaces associated with Dunkl--Schrödinger operators",
  "title_text": "Riesz transform characterization of Hardy spaces associated with Dunkl--Schrödinger operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/dnfzr30ehyagn",
  "venue": "arXiv",
  "versions": []
}