{
  "id": "1102.3995",
  "version": "v1",
  "published": "2011-02-19T15:58:42.000Z",
  "updated": "2011-02-19T15:58:42.000Z",
  "title": "Optimal estimates for harmonic functions in the unit ball",
  "authors": [
    "David Kalaj",
    "Marijan Markovic"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We find the sharp constants $C_p$ and the sharp functions $C_p=C_p(x)$ in the inequality $$|u(x)|\\leq \\frac{C_p}{(1-|x|^2)^{(n-1)/p}}\\|u\\|_{h^p(B^n)}, u\\in h^p(B^n), x\\in B^n,$$ in terms of Gauss hypergeometric and Euler functions. This extends and improves some results of Axler, Bourdon and Ramey (\\cite{ABR}), where they obtained similar results which are sharp only in the cases $p=2$ and $p=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-19T15:58:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31A05"
    ],
    "keywords": [
      "harmonic functions",
      "unit ball",
      "optimal estimates",
      "sharp functions",
      "sharp constants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3995K"
    }
  }
}