{
  "id": "2304.10402",
  "version": "v1",
  "published": "2023-04-20T15:39:08.000Z",
  "updated": "2023-04-20T15:39:08.000Z",
  "title": "On Landau -- Kolmogorov type inequalities for charges and their applications",
  "authors": [
    "Vladyslav Babenko",
    "Vira Babenko",
    "Oleg Kovalenko",
    "Nataliia Parfinovych"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article we prove sharp Landau--Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in $\\mathbb{R}^d$, $d\\geq 1$, that are absolutely continuous with respect to the Lebesgue measure. In addition we solve the Stechkin problem of approximation of the Radon--Nikodym derivative of such charges by bounded operators and two related problems. As an application, we also solve these extremal problems on classes of essentially bounded functions $f$ such that their distributional partial derivative $\\frac{\\partial ^d f}{\\partial x_1\\ldots\\partial x_d}$ belongs to the Sobolev space $W^{1,\\infty}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-20T15:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "41A17",
      "41A44",
      "41A55"
    ],
    "keywords": [
      "application",
      "sharp landau-kolmogorov type inequalities",
      "lebesgue measurable subsets",
      "lebesgue measure",
      "stechkin problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}