{
  "id": "1109.5626",
  "version": "v1",
  "published": "2011-09-26T16:25:55.000Z",
  "updated": "2011-09-26T16:25:55.000Z",
  "title": "Hardy spaces related to Schrödinger operators with potentials which are sums of L^p-functions",
  "authors": [
    "Jacek Dziubański",
    "Marcin Preisner"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We investigate the Hardy space H^1_L associated to the Schr\\\"odinger operator L=-\\Delta+V on R^n, where V=\\sum_{j=1}^d V_j. We assume that each V_j depends on variables from a linear subspace VV_j of \\Rn, dim VV_j \\geq 3, and V_j belongs to L^q(VV_j) for certain q. We prove that there exist two distinct isomorphisms of H^1_L with the classical Hardy space. As a corollary we deduce a specific atomic characterization of H_L^1. We also prove that the space H_L^1 is described by means of the Riesz transforms R_{L,i} = \\partial_i L^{-1/2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-26T16:25:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "35J10",
      "42B35",
      "42B20"
    ],
    "keywords": [
      "hardy spaces",
      "schrödinger operators",
      "potentials",
      "specific atomic characterization",
      "riesz transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.5626D"
    }
  }
}