{
  "id": "1802.06607",
  "version": "v1",
  "published": "2018-02-19T12:25:05.000Z",
  "updated": "2018-02-19T12:25:05.000Z",
  "title": "Harmonic functions, conjugate harmonic functions and the Hardy space $H^1$ in the rational Dunkl setting",
  "authors": [
    "Jean-Philippe Anker",
    "Jacek Dziubański",
    "Agnieszka Hejna"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\\Delta$ be the Dunkl Laplacian on a Euclidean space $\\mathbb{R}^N$. On the half-space $\\mathbb{R}_+\\times\\mathbb{R}^N$, we consider systems of conjugate $(\\partial_t^2+\\Delta_{\\mathbf{x}})$-harmonic functions satisfying an appropriate uniform $L^1$ condition. We prove that the boundary values of such harmonic functions, which constitute the real Hardy space $H^1$, can be characterized in several different ways, namely by means of atoms, Riesz transforms, maximal functions or Littlewood-Paley square functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-19T12:25:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "33C52",
      "35J05",
      "35K08",
      "42B25",
      "42B35",
      "42B37",
      "42C05"
    ],
    "keywords": [
      "rational dunkl setting",
      "conjugate harmonic functions",
      "littlewood-paley square functions",
      "real hardy space",
      "maximal functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}