{
  "id": "2010.08701",
  "version": "v1",
  "published": "2020-10-17T03:04:06.000Z",
  "updated": "2020-10-17T03:04:06.000Z",
  "title": "Pointwise Convergence of Schrödinger means in $\\mathbb{R}^{2}$",
  "authors": [
    "Wenjuan Li",
    "Huiju Wang",
    "Dunyan Yan"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider pointwise convergence of Schr\\\"{o}dinger means $e^{it_{n}\\Delta}f(x)$ for $f \\in H^{s}(\\mathbb{R}^{2})$ and decreasing sequences $\\{t_{n}\\}_{n=1}^{\\infty}$ converging to zero. The main theorem improves the previous results of [Sj\\\"{o}lin, JFAA, 2018] and [Sj\\\"{o}lin-Str\\\"{o}mberg, JMAA, 2020] in $\\mathbb{R}^{2}$. This study is based on investigating properties of Schr\\\"{o}dinger type maximal functions related to hypersurfaces with vanishing Gaussian curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-17T03:04:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "35S10"
    ],
    "keywords": [
      "pointwise convergence",
      "schrödinger means",
      "type maximal functions",
      "main theorem",
      "vanishing gaussian curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}