{
  "id": "1003.5066",
  "version": "v4",
  "published": "2010-03-26T08:03:07.000Z",
  "updated": "2012-06-28T06:46:31.000Z",
  "title": "A Bernstein-type inequality for rational functions in weighted Bergman spaces",
  "authors": [
    "Anton Baranov",
    "Rachid Zarouf"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given $n\\geq1$ and $r\\in[0, 1),$ we consider the set $\\mathcal{R}_{n, r}$ of rational functions having at most $n$ poles all outside of $\\frac{1}{r}\\mathbb{D},$ were $\\mathbb{D}$ is the unit disc of the complex plane. We give an asymptotically sharp Bernstein-type inequality for functions in $\\mathcal{R}_{n, r}\\:$ (as n tends to infinity and r tends to 1-) in weighted Bergman spaces with \"polynomially\" decreasing weights. We also prove that this result can not be extended to weighted Bergman spaces with \"super-polynomially\" decreasing weights.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-06-28T06:46:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted bergman spaces",
      "rational functions",
      "decreasing weights",
      "asymptotically sharp bernstein-type inequality",
      "unit disc"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5066B"
    }
  }
}