{
  "id": "1111.3719",
  "version": "v1",
  "published": "2011-11-16T07:42:02.000Z",
  "updated": "2011-11-16T07:42:02.000Z",
  "title": "A sharp equivalence between $H^\\infty$ functional calculus and square function estimates",
  "authors": [
    "Christian Le Merdy"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let T_t = e^{-tA} be a bounded analytic semigroup on Lp, with 1<p<\\infty. It is known that if A and its adjoint A^* both satisfy square function estimates \\bignorm{\\bigl(\\int_{0}^{\\infty}| A^{1/2} T_t(x)|^2\\, dt\\,\\bigr)^{1/2}_{Lp} \\lesssim \\norm{x} and \\bignorm{\\bigl(\\int_{0}^{\\infty}|A^{*}^{1/2} T_t^*(y)|^2\\, dt\\,\\bigr)^{1/2}_{Lp'} \\lesssim \\norm{y} for x in Lp and y in Lp', then A admits a bounded H^{\\infty}(\\Sigma_\\theta) functional calculus for any \\theta>\\frac{\\pi}{2}. We show that this actually holds true for some \\theta<\\frac{\\pi}{2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-16T07:42:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "47D06"
    ],
    "keywords": [
      "square function estimates",
      "functional calculus",
      "sharp equivalence",
      "bounded analytic semigroup",
      "holds true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3719L"
    }
  }
}