{
  "id": "1310.2262",
  "version": "v1",
  "published": "2013-10-08T20:12:44.000Z",
  "updated": "2013-10-08T20:12:44.000Z",
  "title": "A characterization of Hardy spaces associated with certain Schrödinger operators",
  "authors": [
    "Jacek Dziubański",
    "Jacek Zienkiewicz"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\{K_t\\}_{t>0}$ be the semigroup of linear operators generated by a Schr\\\"odinger operator $-L=\\Delta - V(x)$ on $\\mathbb R^d$, $d\\geq 3$, where $V(x)\\geq 0$ satisfies $\\Delta^{-1} V\\in L^\\infty$. We say that an $L^1$-function $f$ belongs to the Hardy space $H^1_L$ if the maximal function $\\mathcal M_L f(x) = \\sup_{t>0} |K_tf(x)|$ belongs to $L^1(\\mathbb R^d) $. We prove that the operator $(-\\Delta)^{1\\slash 2} L^{-1\\slash 2}$ is an isomorphism of the space $H^1_L$ with the classical Hardy space $H^1(\\mathbb R^d)$ whose inverse is $L^{1\\slash 2} (-\\Delta)^{-1\\slash 2}$. As a corollary we obtain that the space $H^1_L$ is characterized by the Riesz transforms $R_j=\\frac{\\partial}{\\partial x_j}L^{-1\\slash 2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-08T20:12:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "35J10",
      "42B35"
    ],
    "keywords": [
      "hardy spaces",
      "schrödinger operators",
      "characterization",
      "maximal function",
      "riesz transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2262D"
    }
  }
}