{
  "id": "1704.01029",
  "version": "v1",
  "published": "2017-04-04T14:17:43.000Z",
  "updated": "2017-04-04T14:17:43.000Z",
  "title": "The Khintchine Inequality is equivalent to the Mixed $\\left( \\ell_{\\frac{p}{p-1}},\\ell_{2}\\right) $-Littlewood Inequality",
  "authors": [
    "Daniel Núñez-Alarcón",
    "Diana M. Serrano-Rodríguez"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove that the Khintchine Inequality is equivalent to the mixed $\\left( \\ell_{\\frac{p}{p-1}},\\ell_{2}\\right) $-Littlewood inequality. Moreover, we obtain the optimal constants of the Multiple Khintchine inequality. As application, we obtain the optimal constants of the multilinear mixed $\\left( \\ell_{\\frac{p}{p-1}},\\ell_{2}\\right) $-Littlewood inequality, completing the estimates in \\cite{racsam}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-04T14:17:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y60",
      "46G25"
    ],
    "keywords": [
      "littlewood inequality",
      "equivalent",
      "optimal constants",
      "multiple khintchine inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}