{
  "id": "math/0403321",
  "version": "v2",
  "published": "2004-03-19T14:42:48.000Z",
  "updated": "2004-04-27T13:18:22.000Z",
  "title": "Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equations",
  "authors": [
    "Quan Zheng",
    "Xiaohua Yao",
    "Da Fan"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "This paper is concerned with Schr\\\"odinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the $L^p$ estimate of solutions for the initial data belonging to a dense subset of $L^p$ in the case of integrable potentials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-27T13:18:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "42B10"
    ],
    "keywords": [
      "schrödinger equations",
      "convex hypersurfaces",
      "principal operators",
      "free case",
      "corresponding level hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3321Z"
    }
  }
}