{
  "id": "1906.03727",
  "version": "v1",
  "published": "2019-06-09T22:30:52.000Z",
  "updated": "2019-06-09T22:30:52.000Z",
  "title": "On pointwise convergence of Schrödinger means",
  "authors": [
    "Evangelos Dimou",
    "Andreas Seeger"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "For functions in the Sobolev space $H^s$ and decreasing sequences $t_n\\to 0$ we examine convergence almost everywhere of the generalized Schr\\\"odinger means on the real line, given by \\[S^af(x,t_n)=\\exp( it_n (-\\partial_{xx})^{a/2})f(x);\\] here $a>0$, $a\\neq 1$. For decreasing convex sequences we obtain a simple characterization of convergence a.e. for all functions in $H^s$ when $0<s<\\min\\{a/4,1/4\\}$ and $a\\neq 1$. We prove sharp quantitative local and global estimates for the associated maximal functions. We also obtain sharp results for the case $a=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-09T22:30:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger means",
      "pointwise convergence",
      "sharp results",
      "sobolev space",
      "associated maximal functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}