{
  "id": "1909.13319",
  "version": "v1",
  "published": "2019-09-29T16:52:53.000Z",
  "updated": "2019-09-29T16:52:53.000Z",
  "title": "Directional maximal function along the primes",
  "authors": [
    "Laura Cladek",
    "Polona Durcik",
    "Ben Krause",
    "José Madrid"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficiently large annulus, for which the $\\ell^2$ norm of the associated maximal operator with supremum taken over all large scales grows with an epsilon power in the number of vectors. This paper is a follow-up to a prior work on the discrete directional maximal operator along the integers by the first and third author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-29T16:52:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B15"
    ],
    "keywords": [
      "directional maximal function",
      "two-dimensional discrete directional maximal operator",
      "large scales grows",
      "third author",
      "prior work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}