{
  "id": "1910.06857",
  "version": "v1",
  "published": "2019-10-15T15:17:55.000Z",
  "updated": "2019-10-15T15:17:55.000Z",
  "title": "Logarithmic Sobolev inequalities for Dunkl operators",
  "authors": [
    "Andrei Velicu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study several inequalities of log-Sobolev type for Dunkl operators. After proving an equivalent of the classical inequality for the usual Dunkl measure, we also study a number of inequalities for weighted probability Dunkl measures, with weights of the form $e^{-|x|^p}$. These are obtained using the method of $U$-bounds. Poincar\\'e inequalities are obtained as consequences of the log-Sobolev inequality. The connection between Poincar\\'e and log-Sobolev inequalities is further examined, obtaining in particular tight log-Sobolev inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T15:17:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmic sobolev inequalities",
      "dunkl operators",
      "log-sobolev inequality",
      "tight log-sobolev inequalities",
      "usual dunkl measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}