{
  "id": "0901.1455",
  "version": "v1",
  "published": "2009-01-11T16:31:32.000Z",
  "updated": "2009-01-11T16:31:32.000Z",
  "title": "The maximal operator associated to a non-symmetric Ornstein-Uhlenbeck semigroup",
  "authors": [
    "G. Mauceri",
    "L. Noselli"
  ],
  "comment": "20 pages, to appear in J Fourier Anal Appl, available on line at http://www.springerlink.com",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let (H_t) be the Ornstein-Uhlenbeck semigroup on R^d with covariance matrix I and drift matrix \\lambda(R-I), where \\lambda>0 and R is a skew-adjoint matrix and denote by \\gamma_\\infty the invariant measure for (H_t). Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L^2(\\gamma_\\infty). We prove that if the matrix R generates a one-parameter group of periodic rotations then the maximal operator associated to the semigroup is of weak type 1 with respect to the invariant measure. We also prove that the maximal operator associated to an arbitrary normal Ornstein-Uhlenbeck semigroup is bounded on L^p(\\gamma_\\infty) if and only if 1<p\\le \\infty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-11T16:31:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "47D03"
    ],
    "keywords": [
      "maximal operator",
      "non-symmetric ornstein-uhlenbeck semigroup",
      "arbitrary normal ornstein-uhlenbeck semigroup",
      "invariant measure",
      "skew-adjoint matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}