{
  "id": "1908.10183",
  "version": "v1",
  "published": "2019-08-27T13:27:01.000Z",
  "updated": "2019-08-27T13:27:01.000Z",
  "title": "A note on Lusin-type approximation of Sobolev functions on Gaussian spaces",
  "authors": [
    "Alexander Shaposhnikov"
  ],
  "categories": [
    "math.FA",
    "math.MG",
    "math.PR"
  ],
  "abstract": "We extend Shigekawa's Meyer-type inequality in $L^1$ to more general Ornstein-Uhlenbeck operators and establish new approximation results in the sense of Lusin for Sobolev functions $f$ with $|\\nabla f| \\in L\\log L$ on infinite-dimensional spaces equipped with Gaussian measures. The proof relies on some new pointwise estimate for the approximations based on the corresponding semigroup which can be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-27T13:27:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "28C20",
      "46E35"
    ],
    "keywords": [
      "sobolev functions",
      "lusin-type approximation",
      "gaussian spaces",
      "extend shigekawas meyer-type inequality",
      "general ornstein-uhlenbeck operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}