{
  "id": "2005.10909",
  "version": "v1",
  "published": "2020-05-21T21:13:14.000Z",
  "updated": "2020-05-21T21:13:14.000Z",
  "title": "Integration operators in average radial integrability spaces of analytic functions",
  "authors": [
    "Tanausú Aguilar-Hernández",
    "Manuel D. Contreras",
    "Luis Rodríguez-Piazza"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators \\begin{align*} T_g (f)(z)=\\int_{0}^{z} f(w)g'(w)\\ dw \\end{align*} acting on the average radial integrability spaces $RM(p,q)$. For these purposes, we develop different tools such as a description of the bidual of $RM(p,0)$ and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood-Paley type inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T21:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H20",
      "47B33",
      "47D06",
      "46E15",
      "47G10"
    ],
    "keywords": [
      "average radial integrability spaces",
      "integration operators",
      "analytic functions",
      "littlewood-paley type inequalities",
      "weak compactness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}