{
  "id": "1002.1240",
  "version": "v1",
  "published": "2010-02-05T14:56:54.000Z",
  "updated": "2010-02-05T14:56:54.000Z",
  "title": "Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator",
  "authors": [
    "G. Mauceri",
    "S. Meda",
    "P. Sjögren"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In the setting of Euclidean space with the Gaussian measure g, we consider all first-order Riesz transforms associated to the infinitesimal generator of the Ornstein-Uhlenbeck semigroup. These operators are known to be bounded on L^p(g), for 1<p<\\infty. We determine which of them are bounded from H^1(g) to L^1(g) and from L^\\infty(g) to BMO(g). Here H^1(g) and BMO(g) are the spaces introduced in this setting by the first two authors. Surprisingly, we find that the results depend on the dimension of the ambient space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-05T14:56:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B30"
    ],
    "keywords": [
      "first-order riesz transforms",
      "ornstein-uhlenbeck operator",
      "endpoint estimates",
      "euclidean space",
      "ambient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.1240M"
    }
  }
}