{
  "id": "1801.06981",
  "version": "v1",
  "published": "2018-01-22T07:32:25.000Z",
  "updated": "2018-01-22T07:32:25.000Z",
  "title": "Spherical means on the Heisenberg group: Stability of a maximal function estimate",
  "authors": [
    "Theresa C. Anderson",
    "Laura Cladek",
    "Malabika Pramanik",
    "Andreas Seeger"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Consider the surface measure $\\mu$ on a sphere in a nonvertical hyperplane on the Heisenberg group $\\mathbb{H}^n$, $n\\ge 2$, and the convolution $f*\\mu$. Form the associated maximal function $Mf=\\sup_{t>0}|f*\\mu_t|$ generated by the automorphic dilations. We use decoupling inequalities due to Wolff and Bourgain-Demeter to prove $L^p$-boundedness of $M$ in an optimal range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T07:32:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "22E25",
      "43A80",
      "35S30"
    ],
    "keywords": [
      "maximal function estimate",
      "heisenberg group",
      "spherical means",
      "surface measure",
      "associated maximal function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}