{
  "id": "1212.6672",
  "version": "v2",
  "published": "2012-12-29T23:13:48.000Z",
  "updated": "2013-01-02T20:55:49.000Z",
  "title": "A note on the hypercontractivity of the polynomial Bohnenblust--Hille inequality",
  "authors": [
    "Daniel Pellegrino"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ and $m$ a positive integer, we remark that there is a constant $C$ so that, for all $r\\in\\lbrack1,\\frac {2m}{m+1}],$ the supremum of the ratio between the $\\ell_{r}$ norm of the coefficients of any nonzero $m$-homogeneous polynomial $P:\\ell_{\\infty}% ^{n}(\\mathbb{K}) \\rightarrow\\mathbb{K}$ and its supremum norm is dominated by $C^{m}\\cdot n^{(\\frac{m}{r}-\\frac{m+1}{2})}$ and, moreover, we prove that the exponent $\\frac{m}{r}-\\frac{m+1}{2}$ is optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-02T20:55:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial bohnenblust-hille inequality",
      "hypercontractivity",
      "supremum norm",
      "positive integer",
      "coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6672P"
    }
  }
}