{
  "id": "1705.06794",
  "version": "v1",
  "published": "2017-05-18T20:40:46.000Z",
  "updated": "2017-05-18T20:40:46.000Z",
  "title": "Littlewood-Paley-Stein functions for Schrödinger operators",
  "authors": [
    "El Maati Ouhabaz"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study boundedness on $L^p(R^d)$ of vertical Littlewood-Paley-Stein functions for Schr\\\"odinger operators $-\\Delta + V$ with nonnegative potential $V$. These functions are proved to be bounded on $L^p$ for all $p \\in (1, 2]$. The situation for $p > 2$ is different. We prove for a class of potentials that the boundedness on $L^p$ for some $p > d$ holds if and only if $V= 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-18T20:40:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger operators",
      "study boundedness",
      "vertical littlewood-paley-stein functions",
      "nonnegative potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}