{
  "id": "1901.04458",
  "version": "v1",
  "published": "2019-01-14T18:44:43.000Z",
  "updated": "2019-01-14T18:44:43.000Z",
  "title": "Sharp Constants of Approximation Theory. II. Invariance Theorems and Multivariate Inequalities of Different Metrics",
  "authors": [
    "Michael I. Ganzburg"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for algebraic polynomials on the unit sphere and the unit ball in $\\R^m$ and the corresponding constants for entire functions of spherical type on $\\R^m$. Certain relations in the univariate weighted spaces are discussed as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-14T18:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "41A63",
      "26D10"
    ],
    "keywords": [
      "sharp constants",
      "invariance theorems",
      "approximation theory",
      "multivariate inequalities",
      "multivariate markov-bernstein-nikolskii type inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}