{
  "id": "2008.03093",
  "version": "v1",
  "published": "2020-08-07T11:43:53.000Z",
  "updated": "2020-08-07T11:43:53.000Z",
  "title": "A Note on Non-tangential Convergence for Schrödinger Operators",
  "authors": [
    "Wenjuan Li",
    "Huiju Wang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The goal of this note is to establish non-tangential convergence results for Schr\\\"{o}dinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the initial data which implies convergence. As a consequence, we obtain a upper bound for $p$ such that the Schr\\\"{o}dinger maximal function is bounded from $H^{s}(\\mathbb{R}^{n})$ to $L^{p}(\\mathbb{R}^{n})$ for any $s > \\frac{n}{2(n+1)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-07T11:43:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "35S10"
    ],
    "keywords": [
      "schrödinger operators",
      "establish non-tangential convergence results",
      "approach region",
      "initial data",
      "implies convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}