{
  "id": "1702.07626",
  "version": "v1",
  "published": "2017-02-24T15:24:54.000Z",
  "updated": "2017-02-24T15:24:54.000Z",
  "title": "Restricted averaging operators to cones over finite fields",
  "authors": [
    "Doowon Koh",
    "Chun-Yen Shen",
    "Seongjun Yeom"
  ],
  "comment": "20 pages, No figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate the sharp L^p\\to L^r estimates for the restricted averaging operator A_C over the cone C of the d-dimensional vector space F_q^d over the finite field F_q with q elements. The restricted averaging operator A_C for the cone C is defined by the relation that A_Cf=f\\ast \\sigma |_C, where \\sigma denotes the normalized surface measure on the cone C, and f is a complex valued function on the space F_q^d with the normalized counting measure dx. In the previous work, the sharp boundedness of A_C was obtained in odd dimensions d\\ge 3 but partial results were only given in even dimensions d\\ge 4. In this paper we prove the optimal estimates in even dimensions d\\ge 6 in the case when the cone C\\subset F_q^d contains a d/2 dimensional subspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-24T15:24:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B05"
    ],
    "keywords": [
      "restricted averaging operator",
      "finite field",
      "d-dimensional vector space",
      "optimal estimates",
      "complex valued function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}