{
  "id": "0809.4054",
  "version": "v1",
  "published": "2008-09-23T23:46:14.000Z",
  "updated": "2008-09-23T23:46:14.000Z",
  "title": "A sharp inequality for the Strichartz norm",
  "authors": [
    "Emanuel Carneiro"
  ],
  "comment": "15 pages. Submitted",
  "journal": "International Mathematics Research Notices, p. 3127-3145, 2009",
  "doi": "10.1093/imrn/rnp045",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $u:\\R \\times \\R^n \\to \\C$ be the solution of the linear Schr\\\"odinger equation $iu_t + \\Delta u =0$ with initial data $u(0,x) = f(x)$. In the first part of this paper we obtain a sharp inequality for the Strichartz norm $\\|u(t,x)\\|_{L^{2k}_tL^{2k}_x(\\R \\times\\R^n)}$, where $k\\in \\Z$, $k \\geq 2$ and $(n,k) \\neq (1,2)$, that admits only Gaussian maximizers. As corollaries we obtain sharp forms of the classical Strichartz inequalities in low dimensions (works of Foschi and Hundertmark - Zharnitsky) and also sharp forms of some Sobolev-Strichartz inequalities. In the second part of the paper we express Foschi's sharp inequalities for the Schr\\\"odinger and wave equations in the broader setting of sharp restriction/extension estimates for the paraboloid and the cone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-23T23:46:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A44",
      "42A05"
    ],
    "keywords": [
      "sharp inequality",
      "strichartz norm",
      "sharp forms",
      "express foschis sharp inequalities",
      "sharp restriction/extension estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4054C"
    }
  }
}