{
  "id": "0911.2313",
  "version": "v1",
  "published": "2009-11-12T08:13:31.000Z",
  "updated": "2009-11-12T08:13:31.000Z",
  "title": "Riesz meets Sobolev",
  "authors": [
    "Thierry Coulhon",
    "Adam Sikora"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the $L^p$ boundedness, $p>2$, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-12T08:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J35",
      "42B20",
      "46E35"
    ],
    "keywords": [
      "riesz meets sobolev",
      "heat kernel gradient upper estimate",
      "lower gaussian heat kernel estimates",
      "complete non-compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.2313C"
    }
  }
}