{
  "id": "1401.6997",
  "version": "v1",
  "published": "2014-01-27T20:36:17.000Z",
  "updated": "2014-01-27T20:36:17.000Z",
  "title": "Weak version of restriction estimates for spheres and paraboloids in finite fields",
  "authors": [
    "Hunseok Kang",
    "Doowon Koh"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study L^p-L^r restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension $d$ is even, then it is conjectured that the L^{(2d+2)/(d+3)}-L^2 Stein-Tomas restriction result can be improved to the L^{(2d+4)/(d+4)}-L^2 estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured L^p-L^2 restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in $d$ dimensions and those for homogeneous varieties in (d+1)dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-27T20:36:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05",
      "43A32",
      "43A15"
    ],
    "keywords": [
      "finite fields",
      "weak version",
      "paraboloids",
      "stein-tomas restriction result",
      "restriction estimate holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6997K"
    }
  }
}