{
  "id": "1102.5467",
  "version": "v1",
  "published": "2011-02-27T02:03:36.000Z",
  "updated": "2011-02-27T02:03:36.000Z",
  "title": "Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces",
  "authors": [
    "Hua Wang"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $L=-\\Delta+V$ be a Schr\\\"odinger operator acting on $L^2(\\mathbb R^n)$, $n\\ge1$, where $V\\not\\equiv 0$ is a nonnegative locally integrable function on $\\mathbb R^n$. In this article, we will introduce weighted Hardy spaces $H^p_L(w)$ associated with $L$ by means of the area integral function and study their atomic decomposition theory. We also show that the Riesz transform $\\nabla L^{-1/2}$ associated with $L$ is bounded from our new space $H^p_L(w)$ to the classical weighted Hardy space $H^p(w)$ when $\\frac{n}{n+1}<p<1$ and$w\\in A_1\\cap RH_{(2/p)'}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-27T02:03:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "42B20",
      "42B30"
    ],
    "keywords": [
      "riesz transforms",
      "schrödinger operators acting",
      "area integral function",
      "atomic decomposition theory",
      "classical weighted hardy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5467W"
    }
  }
}