{
  "id": "1501.00965",
  "version": "v1",
  "published": "2015-01-05T20:33:25.000Z",
  "updated": "2015-01-05T20:33:25.000Z",
  "title": "On the optimal constants of the Bohnenblust--Hille and Hardy--Littlewood inequalities",
  "authors": [
    "Daniel Pellegrino"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We find the optimal constants of the generalized Bohnenblust--Hille inequality for $m$-linear forms over $\\mathbb{R}$ and with multiple exponents $ \\left( 1,2,...,2\\right)$, sometimes called mixed $\\left( \\ell _{1},\\ell _{2}\\right) $-Littlewood inequality. We show that these optimal constants are precisely $\\left( \\sqrt{2}\\right) ^{m-1}$ and this is somewhat surprising since a series of recent papers have shown that the constants of the Bohnenblust--Hille inequality have a sublinear growth, and in several cases the same growth was obtained for the constants of the generalized Bohnenblust--Hille inequality. This result answers a question raised by Albuquerque et al. (2013) in a paper published in 2014 in the Journal of Functional Analysis. We also improve the best known constants of the generalized Hardy--Littlewood inequality in such a way that an unnatural behavior of the old estimates (that will be clear along the paper) does not happen anymore.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-05T20:33:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal constants",
      "generalized bohnenblust-hille inequality",
      "happen anymore",
      "linear forms",
      "result answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150100965P"
    }
  }
}