{
  "id": "2003.02077",
  "version": "v1",
  "published": "2020-03-04T13:41:39.000Z",
  "updated": "2020-03-04T13:41:39.000Z",
  "title": "Multiplier theorems via martingale transforms",
  "authors": [
    "Rodrigo Bañuelos",
    "Fabrice Baudoin",
    "Li Chen",
    "Yannick Sire"
  ],
  "comment": "The paper generalizes results and extends the framework and scope of the paper arXiv:1802.02410",
  "categories": [
    "math.PR",
    "math.AP",
    "math.FA"
  ],
  "abstract": "We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp $L^p$ bounds for second order Riesz transforms by a liming argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-04T13:41:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martingale transforms",
      "multiplier theorems",
      "second order riesz transforms",
      "main idea",
      "probabilistic proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}