{
  "id": "1103.4752",
  "version": "v1",
  "published": "2011-03-24T12:42:18.000Z",
  "updated": "2011-03-24T12:42:18.000Z",
  "title": "The boundedness of some singular integral operators on weighted Hardy spaces associated with Schrödinger operators",
  "authors": [
    "Hua Wang"
  ],
  "comment": "21 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 paper, we first define molecules for weighted Hardy spaces $H^p_L(w)$($0<p\\le1$) associated to $L$ and establish their molecular characterizations. Then by using the atomic decomposition and molecular characterization of $H^p_L(w)$, we will show that the imaginary power $L^{i\\gamma}$ is bounded on $H^p_L(w)$ for $n/{(n+1)}<p\\le1$, and the fractional integral operator $L^{-\\alpha/2}$ is bounded from $H^p_L(w)$ to $H^q_L(w^{q/p})$, where $0<\\alpha<\\min\\{n/2,1\\}$, $n/{(n+1)}<p\\le n/{(n+\\alpha)}$ and $1/q=1/p-\\alpha/n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-24T12:42:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "42B20",
      "42B30"
    ],
    "keywords": [
      "weighted hardy spaces",
      "singular integral operators",
      "schrödinger operators",
      "boundedness",
      "molecular characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4752W"
    }
  }
}