{
  "id": "1602.05207",
  "version": "v1",
  "published": "2016-02-16T21:17:51.000Z",
  "updated": "2016-02-16T21:17:51.000Z",
  "title": "The variation and Kantorovich distances between distributions of polynomials and a fractional analog of the Hardy--Landau--Littlewood inequality",
  "authors": [
    "Vladimir I. Bogachev",
    "Egor D. Kosov",
    "Georgii I. Zelenov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Our first main result is an upper bound on the total variation distance between two probability measures on $\\mathbb{R}^k$ via the Kantorovich distance between them and a certain Besov--Nikol'skii norm of their difference. Our second result asserts that the distribution of a non-constant polynomial of order $d$ (possibly, in infinitely many variables) with respect to a Gaussian measure always belongs to the Besov--Nikol'skii space $N^{1/d}$, and an analogous result holds for polynomial mappings with values in $\\mathbb{R}^k$. Finally, we consider the total variation distance between the distributions of two random $k$-dimensional vectors composed of polynomials of order $d$ in Gaussian variables. This distance is estimated by a fractional power of the Kantorovich distance with an exponent depending only on $d$ and $k$, but not on the number of variables of the considered polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-16T21:17:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kantorovich distance",
      "polynomial",
      "fractional analog",
      "hardy-landau-littlewood inequality",
      "total variation distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205207B"
    }
  }
}