{
  "id": "1801.07214",
  "version": "v1",
  "published": "2018-01-22T17:41:09.000Z",
  "updated": "2018-01-22T17:41:09.000Z",
  "title": "Endpoint results for the Riesz transform of the Ornstein-Uhlenbeck operator",
  "authors": [
    "Tommaso Bruno"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we introduce a new atomic Hardy space $X^1(\\gamma)$ adapted to the Gauss measure $\\gamma$, and prove the boundedness of the first order Riesz transform associated with the Ornstein-Uhlenbeck operator from $X^1(\\gamma)$ to $L^1(\\gamma)$. We also provide a new, short and almost self-contained proof of its weak-type $(1,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T17:41:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ornstein-uhlenbeck operator",
      "endpoint results",
      "first order riesz transform",
      "atomic hardy space",
      "gauss measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}