{
  "id": "2105.03520",
  "version": "v1",
  "published": "2021-05-07T22:12:33.000Z",
  "updated": "2021-05-07T22:12:33.000Z",
  "title": "Averages and maximal averages over Product j-varieties in finite fields",
  "authors": [
    "Doowon Koh",
    "Sujin Lee"
  ],
  "comment": "13 pages, no figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study both averaging and maximal averaging problems for Product $j$-varieties defined by $\\Pi_j=\\{x\\in \\mathbb F_q^d: \\prod_{k=1}^d x_k=j\\}$ for $j\\in \\mathbb F_q^*,$ where $\\mathbb F_q^d$ denotes a $d$-dimensional vector space over the finite field $\\mathbb F_q$ with $q$ elements. We prove the sharp $L^p\\to L^r$ boundedness of averaging operators associated to Product $j$-varieties. We also obtain the optimal $L^p$ estimate for a maximal averaging operator related to a family of Product $j$-varieties $\\{\\Pi_j\\}_{j\\in \\mathbb F_q^*}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-07T22:12:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C10",
      "42B05",
      "11T23"
    ],
    "keywords": [
      "finite field",
      "product j-varieties",
      "maximal averages",
      "dimensional vector space",
      "maximal averaging problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}