{
  "id": "1611.08413",
  "version": "v1",
  "published": "2016-11-25T10:48:28.000Z",
  "updated": "2016-11-25T10:48:28.000Z",
  "title": "Improved L$^p$-Poincaré inequalities on the hyperbolic space",
  "authors": [
    "Elvise Berchio",
    "Debdip Ganguly",
    "Gabriele Grillo"
  ],
  "categories": [
    "math.FA",
    "math.DG"
  ],
  "abstract": "We investigate the possibility of improving the $p$-Poincar\\'e inequality $\\|\\nabla_{\\hn} u\\|_p \\ge \\Lambda_p \\|u\\|_p$ on the hyperbolic space, where $p>2$ and $\\Lambda_p:=[(N-1)/p]^{p}$ is the best constant for which such inequality holds. We prove several different, and independent, improved inequalities, one of which is a Poincar\\'e-Hardy inequality, namely an improvement of the best $p$-Poincar\\'e inequality in terms of the Hardy weight $r^{-p}$, $r$ being geodesic distance from a given pole. Certain Hardy-Maz'ya-type inequalities in the Euclidean half-space are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-25T10:48:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic space",
      "poincare inequality",
      "poincare-hardy inequality",
      "euclidean half-space",
      "best constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}