{
  "id": "1106.3288",
  "version": "v3",
  "published": "2011-06-16T17:45:58.000Z",
  "updated": "2012-06-25T18:40:47.000Z",
  "title": "Boundedness of Maximal Operators of Schrödinger Type with Complex Time",
  "authors": [
    "Andrew D. Bailey"
  ],
  "comment": "12 pages. One further minor correction. To appear in the Revista Matem\\'atica Iberoamericana",
  "journal": "Rev. Mat. Iberoam. 29 (2013), no. 2",
  "doi": "10.4171/RMI/729",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Results of P. Sj\\\"olin and F. Soria on the Schr\\\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \\geq 0$ for which boundedness from the Sobolev space $H^s(\\mathbb{R})$ into $L^2(\\mathbb{R})$ occurs. Bounds are established for not only the Schr\\\"odinger maximal operator, but further for a general class of maximal operators corresponding to solution operators for certain dispersive PDEs. As a consequence of additional bounds on these maximal operators from $H^s(\\mathbb{R})$ into $L^2([-1, 1])$, sharp results on the pointwise almost everywhere convergence of the solutions of these PDEs to their initial data are determined.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-25T18:40:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "42B25",
      "42B37"
    ],
    "keywords": [
      "schrödinger type",
      "complex time",
      "boundedness",
      "initial data",
      "sobolev space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3288B"
    }
  }
}