{
  "abstract": "We prove a Hörmander multiplier theorem for the Dunkl transform associated with an arbitrary finite reflection group. Uniform $H^σ(\\mathbb{R}^N)$ bounds for the normalised dyadic pieces of a measurable symbol, with $σ>\\mathbf N/2$ and $\\mathbf N$ the homogeneous dimension, imply $L^p(dω)$ boundedness for $1<p<\\infty$ and weak type $(1,1)$. No radiality or reflection-group invariance is assumed, and the dyadic pieces may meet the reflecting hyperplanes. The main new estimate controls the Dunkl kernel $E_κ(iξ,x)$ and its first Euclidean derivatives in $x$, uniformly near arbitrary intersections of reflecting hyperplanes. Here $ξ$ lies in a fixed compact annulus. Writing $w_κ$ for the Dunkl weight and $Ω_κ$ for its inhomogeneous counterpart, it gives the bound $CΩ_κ(x)^{-1/2}w_κ(ξ)^{-1/2}$. The proof decomposes each root contribution into Hermitian two-dimensional blocks, applies oscillatory changes of variables near the rootwise transition points, and uses a commutator identity to cancel the non-integrable phase derivative. Chamber lifting also yields endpoint bounds for the pullbacks of the componentwise Coifman--Weiss atomic $H^1$ space and the corresponding BMO space on a fixed chamber.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14298",
  "author_total": 4,
  "authors": [
    {
      "name": "Der-Chen Chang"
    },
    {
      "name": "Ji Li"
    },
    {
      "name": "Chaojie Wen"
    },
    {
      "name": "Liangchuan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pj0cyzacam0j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14298",
  "fulltext_url": null,
  "id": "3pj0cyzacam0j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14298",
  "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": "W7213290730",
  "pdf_url": "https://arxiv.org/pdf/2609.14298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pj0cyzacam0j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-radial Dunkl multipliers at the $L^2$-Sobolev threshold",
  "title_text": "Non-radial Dunkl multipliers at the L^2-Sobolev threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3pj0cyzacam0j",
  "venue": "arXiv",
  "versions": []
}