{
  "id": "1607.08746",
  "version": "v1",
  "published": "2016-07-29T09:43:47.000Z",
  "updated": "2016-07-29T09:43:47.000Z",
  "title": "On the Green function and Poisson integrals of the Dunkl Laplacian",
  "authors": [
    "Piotr Graczyk",
    "Tomasz Luks",
    "Margit Rösler"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\\Delta_k$ in $\\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\\Delta_k$-subharmonic functions and Hardy-Stein identities for the Poisson integrals of $\\Delta_k$. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in $\\mathbb{R}^d$. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T09:43:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B05",
      "31B25",
      "60J50",
      "42B30",
      "51F15"
    ],
    "keywords": [
      "green function",
      "poisson integrals",
      "dunkl laplacian",
      "newton potential kernel",
      "poisson-jensen formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}