{
  "id": "1211.3386",
  "version": "v2",
  "published": "2012-11-14T19:13:24.000Z",
  "updated": "2013-11-14T16:59:55.000Z",
  "title": "Characterization of the restricted type spaces R(X)",
  "authors": [
    "Javier Soria",
    "Pedro Tradacete"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We study functorial properties of the spaces $R(X)$, introduced in [Studia Math. 197 (2010), 69-79] as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space $\\Lambda_{\\varphi}$ so that the equation $R(X)=\\Lambda_{\\varphi}$ has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that if $R(X)=\\Lambda_{\\varphi}$, then we can always take $X$ to be the minimal r.i. Banach range space for the Hardy operator defined in $\\Lambda_{\\varphi}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-14T16:59:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "46E30"
    ],
    "keywords": [
      "restricted type spaces",
      "characterization",
      "hardy operator minus",
      "minimal lorentz space",
      "banach range space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3386S"
    }
  }
}