{
  "id": "1604.06323",
  "version": "v1",
  "published": "2016-04-21T14:30:51.000Z",
  "updated": "2016-04-21T14:30:51.000Z",
  "title": "Optimal constants for the mixed $\\left(\\ell_{\\frac{p}{p-1}}, \\ell_2\\right)$-Littlewood inequality",
  "authors": [
    "Tony Nogueira"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For $p > 2.18006$ we prove that optimal constants for the mixed $\\left( \\ell _{\\frac{p}{p-1}},\\ell _{2}\\right) $-Littlewood inequality for real-valued $m$% -linear forms on $\\ell _{p}\\times c_{0}\\times \\dots \\times c_{0}$ are $% \\left( 2^{\\frac{1}{2}-\\frac{1}{p}}\\right) ^{m-1}.$ As far as we know, this is the first example of Hardy--Littlewood inequalities for $m$-linear forms with optimal constants with exponential growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-21T14:30:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal constants",
      "littlewood inequality",
      "linear forms",
      "first example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160406323N"
    }
  }
}