{
  "id": "1910.06245",
  "version": "v1",
  "published": "2019-10-14T16:20:36.000Z",
  "updated": "2019-10-14T16:20:36.000Z",
  "title": "Semigroup and Riesz transform for the Dunkl- Schrödinger operators",
  "authors": [
    "Béchir Amri",
    "Amel Hammi"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "Let $L_k=-\\Delta_k+V$ be the Dunk- Schr\\\"{o}dinger operators, where $\\Delta_k=\\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $R_j= T_j L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is of weak type $(1,1)$ and then is bounded on $L^p(\\mathbb{R}^d,d\\mu_k(x))$ for $1<p\\leq 2$. The second pat is devoted to the $L^p$ smoothing of the semigroup generated by $L_k$, when $V$ belongs to the standard Koto class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-14T16:20:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riesz transform",
      "schrödinger operators",
      "dunkl laplace operator",
      "standard koto class",
      "nonnegative potential function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}