{
  "id": "1805.03764",
  "version": "v1",
  "published": "2018-05-10T00:48:21.000Z",
  "updated": "2018-05-10T00:48:21.000Z",
  "title": "Capacities, removable sets and $L^p$-uniqueness on Wiener spaces",
  "authors": [
    "Michael Hinz",
    "Seunghyun Kang"
  ],
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "We prove the equivalence of two different types of capacities in abstract Wiener spaces. This yields a criterion for the $L^p$-uniqueness of the Ornstein-Uhlenbeck operator and its integer powers defined on suitable algebras of functions vanishing in a neighborhood of a given closed set $\\Sigma$ of zero Gaussian measure. To prove the equivalence we show the $W^{r,p}(B,\\mu)$-boundedness of certain smooth nonlinear truncation operators acting on potentials of nonnegative functions. We also give connections to Gaussian Hausdorff measures. Roughly speaking, if $L^p$-uniqueness holds then the 'removed' set $\\Sigma$ must have sufficiently large codimension, in the case of the Ornstein-Uhlenbeck operator for instance at least $2p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-10T00:48:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A12",
      "31E05",
      "31C15",
      "35J25",
      "35J40",
      "47B25",
      "47B38",
      "47N30",
      "60H07",
      "60J45"
    ],
    "keywords": [
      "removable sets",
      "uniqueness",
      "capacities",
      "ornstein-uhlenbeck operator",
      "zero gaussian measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}