{
  "id": "1111.3253",
  "version": "v2",
  "published": "2011-11-14T15:48:24.000Z",
  "updated": "2011-11-18T12:02:28.000Z",
  "title": "Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars",
  "authors": [
    "Diogo Diniz",
    "Gustavo Muñoz-Fernández",
    "Daniel Pellegrino",
    "Juan B. Seoane-Sepúlveda"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer $N$ and every $m$-linear mapping $T:\\ell_{\\infty}^{N}\\times...\\times\\ell_{\\infty}^{N}\\rightarrow \\mathbb{R}$ one has (\\sum\\limits_{i_{1},...,i_{m}=1}^{N}|T(e_{i_{^{1}}},...,e_{i_{m}})|^{\\frac{2m}{m+1}})^{\\frac{m+1}{2m}}\\leq C_{m}\\VertT\\Vert, for some positive constant $C_{m}$. Since then, several authors obtained upper estimates for the values of $C_{m}$. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for $C_{m}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-18T12:02:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bohnenblust-hille inequality",
      "real scalars",
      "lower bounds",
      "upper estimates",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3253D"
    }
  }
}