{
  "id": "1106.4960",
  "version": "v1",
  "published": "2011-06-24T12:58:58.000Z",
  "updated": "2011-06-24T12:58:58.000Z",
  "title": "Hardy spaces associated with Schrodinger operators on the Heisenberg group",
  "authors": [
    "Chin-Cheng Lin",
    "Heping Liu",
    "Yu Liu"
  ],
  "comment": "42 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $L= -\\Delta_{\\mathbb{H}^n}+V$ be a Schr\\\"odinger operator on the Heisenberg group $\\mathbb{H}^n$, where $\\Delta_{\\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_{\\frac{Q}{2}}$ and $Q$ is the homogeneous dimension of $\\mathbb{H}^n$. The Riesz transforms associated with the Schr\\\"odinger operator $L$ are bounded from $L^1(\\mathbb{H}^n)$ to $L^{1,\\infty}(\\mathbb{H}^n)$. The $L^1$ integrability of the Riesz transforms associated with $L$ characterizes a certain Hardy type space denoted by $H^1_L(\\mathbb{H}^n)$ which is larger than the usual Hardy space $H^1(\\mathbb{H}^n)$. We define $H^1_L(\\mathbb{H}^n)$ in terms of the maximal function with respect to the semigroup $\\big \\{e^{-s L}:\\; s>0 \\big\\}$, and give the atomic decomposition of $H^1_L(\\mathbb{H}^n)$. As an application of the atomic decomposition theorem, we prove that $H^1_L(\\mathbb{H}^n)$ can be characterized by the Riesz transforms associated with $L$. All results hold for stratified groups as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-24T12:58:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy spaces",
      "heisenberg group",
      "schrodinger operators",
      "riesz transforms",
      "atomic decomposition theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4960L"
    }
  }
}