{
  "id": "1703.01015",
  "version": "v1",
  "published": "2017-03-03T02:17:22.000Z",
  "updated": "2017-03-03T02:17:22.000Z",
  "title": "Hausdorff operators on holomorphic Hardy spaces and applications",
  "authors": [
    "Ha Duy Hung",
    "Thai Thuan Quang",
    "Luong Dang Ky"
  ],
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "The aim of this paper is to characterize the nonnegative functions $\\varphi$ defined on $(0,\\infty)$ for which the Hausdorff operator $$\\mathscr H_\\varphi f(z)= \\int_0^\\infty f\\left(\\frac{z}{t}\\right)\\frac{\\varphi(t)}{t}dt$$ is bounded on the Hardy spaces of the upper half-plane $\\mathcal H_a^p(\\mathbb C_+)$, $p\\in[1,\\infty]$. The corresponding operator norms and their applications are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-03T02:17:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "42B30",
      "46E15"
    ],
    "keywords": [
      "holomorphic hardy spaces",
      "hausdorff operator",
      "applications",
      "upper half-plane",
      "corresponding operator norms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}