{
  "id": "2403.13149",
  "version": "v1",
  "published": "2024-03-19T20:53:25.000Z",
  "updated": "2024-03-19T20:53:25.000Z",
  "title": "Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter",
  "authors": [
    "Michael I Ganzburg",
    "Miquel Saucedo",
    "Sergey Tikhonov"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $\\|f^{(s)}\\|_q \\lesssim C(s, p, q)\\left\\|f\\right\\|_p,\\,0<p<q \\leq\\infty$, for trigonometric polynomials and entire functions of exponential type. We obtain the optimal behavior of the constant with respect to the smoothness parameter $s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-19T20:53:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A17",
      "42A05"
    ],
    "keywords": [
      "bernstein-nikolskii inequality",
      "smoothness parameter",
      "optimality",
      "trigonometric polynomials",
      "entire functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}