{
  "id": "1712.03952",
  "version": "v1",
  "published": "2017-12-10T14:07:11.000Z",
  "updated": "2017-12-10T14:07:11.000Z",
  "title": "Characterization of temperatures associated to Schrödinger operators with initial data in Morrey spaces",
  "authors": [
    "Qiang Huang",
    "Chao Zhang"
  ],
  "comment": "15 pages. arXiv admin note: substantial text overlap with arXiv:1710.01160",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $\\L$ be a Schr\\\"odinger operator of the form $\\L=-\\Delta+V$ acting on $L^2(\\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\\\"older class $B_q$ for some $q\\geq n.$ Let $L^{p,\\lambda}(\\mathbb{R}^{n})$, $0\\le \\lambda<n$ denote the Morrey space on $\\mathbb{R}^{n}$. In this paper, we will show that a function $f\\in L^{2,\\lambda}(\\mathbb{R}^{n})$ is the trace of the solution of ${\\mathbb L}u=u_{t}+{\\L}u=0, u(x,0)= f(x),$ where $u$ satisfies a Carleson-type condition \\begin{eqnarray*} \\sup_{x_B, r_B} r_B^{-\\lambda}\\int_0^{r_B^2}\\int_{B(x_B, r_B)} |\\nabla u(x,t)|^2 {dx dt} \\leq C <\\infty. \\end{eqnarray*} Conversely, this Carleson-type condition characterizes all the ${\\mathbb L}$-carolic functions whose traces belong to the Morrey space $L^{2,\\lambda}(\\mathbb{R}^{n})$ for all $0\\le \\lambda<n$. This result extends the analogous characterization founded by Fabes and Neri for the classical BMO space of John and Nirenberg.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-10T14:07:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B37",
      "35J10",
      "47F05"
    ],
    "keywords": [
      "morrey space",
      "schrödinger operators",
      "initial data",
      "characterization",
      "temperatures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}