{
  "id": "1804.09260",
  "version": "v1",
  "published": "2018-04-24T21:09:40.000Z",
  "updated": "2018-04-24T21:09:40.000Z",
  "title": "$\\ell^p$-improving for discrete spherical averages",
  "authors": [
    "Kevin Hughes"
  ],
  "comment": "10 pages, Comments welcome =)",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we prove $\\ell^p$-improving estimates for the discrete spherical averages and some of their generalizations. At first glance this problem appears trivial, but upon further examination we obtain interesting, nontrivial bounds. As an application we give a new estimate for the discrete spherical maximal function in four dimensions. We conclude by introducing a principle to describe the analogy with Littman's result for continuous spherical averages.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T21:09:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete spherical averages",
      "problem appears trivial",
      "discrete spherical maximal function",
      "first glance",
      "nontrivial bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}