{
  "id": "1301.1539",
  "version": "v4",
  "published": "2013-01-08T14:08:13.000Z",
  "updated": "2015-02-11T23:40:52.000Z",
  "title": "On the optimality of the hypercontractivity of the complex Bohnenblust--Hille inequality",
  "authors": [
    "J. R. Campos",
    "G. A. Muñoz-Fernández",
    "D. Pellegrino",
    "J. B. Seoane-Sepúlveda"
  ],
  "comment": "The results in it are either obsolete or they were recently improved",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main motivation of this paper is the following open problem: Is the hypercontractivity of the \\emph{complex} polynomial Bohnenblust--Hille inequality an optimal result? We show that the solution to this problem has a close connection with the searching of the optimal constants for the \\emph{real} polynomial Bohnenblust--Hille inequality. So we are lead to a detailed study of the hypercontractivity constants for real scalars. In fact we study two notions of constants of hypercontractivity: absolute ($H_{a,\\mathbb{R}}$) and asymptotic ($H_{\\infty,\\mathbb{R}}$). Among other results, our estimates combined with recent results from \\cite{CMPS} show that \\[ 1.5098<H_{\\infty,\\mathbb{R}}<2.829 \\quad \\text{and} \\quad 1.6561<H_{a,\\mathbb{R}}<3.296. \\]",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-11T14:48:22.000Z",
      "comment": "This preprint does no longer exist as a single manuscript. It is now part of the preprint entitled \"The optimal asymptotic hypercontractivity constant of the real polynomial Bohnenblust-Hille inequality is 2\" (arXiv reference 1209.4632). arXiv admin note: text overlap with arXiv:1209.4632",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-02-11T23:40:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G25",
      "30B50"
    ],
    "keywords": [
      "complex bohnenblust-hille inequality",
      "polynomial bohnenblust-hille inequality",
      "optimality",
      "optimal result",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1539C"
    }
  }
}