{
  "id": "1702.03486",
  "version": "v1",
  "published": "2017-02-12T04:17:28.000Z",
  "updated": "2017-02-12T04:17:28.000Z",
  "title": "Norm of the Hausdorff operator on the real Hardy space $H^1(\\mathbb R)$",
  "authors": [
    "Ha Duy Hung",
    "Luong Dang Ky",
    "Thai Thuan Quang"
  ],
  "comment": "Complex Anal. Oper. Theory (to appear)",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\varphi$ be a nonnegative integrable function on $(0,\\infty)$. It is well-known that the Hausdorff operator $\\mathcal H_\\varphi$ generated by $\\varphi$ is bounded on the real Hardy space $H^1(\\mathbb R)$. The aim of this paper is to give the exact norm of $\\mathcal H_\\varphi$. More precisely, we prove that $$\\|\\mathcal H_\\varphi\\|_{H^1(\\mathbb R)\\to H^1(\\mathbb R)}= \\int_0^\\infty \\varphi(t)dt.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-12T04:17:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real hardy space",
      "hausdorff operator",
      "exact norm",
      "nonnegative integrable function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}