{
  "id": "1409.5861",
  "version": "v1",
  "published": "2014-09-20T06:31:56.000Z",
  "updated": "2014-09-20T06:31:56.000Z",
  "title": "An extension of the Beckner's type Poincaré inequality to convolution measures on abstract Wiener spaces",
  "authors": [
    "Paolo Da Pelo",
    "Alberto Lanconelli",
    "Aurel I. Stan"
  ],
  "comment": "18 pages. arXiv admin note: text overlap with arXiv:1409.3447",
  "categories": [
    "math.PR"
  ],
  "abstract": "We generalize the Beckner's type Poincar\\'e inequality \\cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\\mu\\star\\nu$, where $\\mu$ is the reference Gaussian measure and $\\nu$ is a probability measure satisfying a certain integrability condition. As the Beckner inequality interpolates between the Poincar\\'e and logarithmic Sobolev inequalities, we utilize a family of products for functions which interpolates between the usual point-wise multiplication and the Wick product. Our approach is based on the positivity of a quadratic form involving Wick powers and integration with respect to those convolution measures. Our dimension-independent results are compared with some very recent findings in the literature. In addition, we prove that in the finite dimensional case the class of densities of convolutions measures satisfies a point-wise covariance inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-20T06:31:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60H30"
    ],
    "keywords": [
      "abstract wiener space",
      "convolution measures",
      "beckners type poincare inequality",
      "probability measure",
      "convolutions measures satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5861D"
    }
  }
}