{
  "id": "1506.06862",
  "version": "v1",
  "published": "2015-06-23T05:07:53.000Z",
  "updated": "2015-06-23T05:07:53.000Z",
  "title": "Rademacher functions in Morrey spaces",
  "authors": [
    "Sergei V. Astashkin",
    "Lech Maligranda"
  ],
  "comment": "submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "The Rademacher functions are investigated in the Morrey spaces M(p,w) on [0,1] for 1 \\le p <\\infty and weight w being a quasi-concave function. They span l_2 space in M(p,w) if and only if the weight w is smaller than the function log_2^{-1/2}(2/t) on (0,1). Moreover, if 1 < p < \\infty the Rademacher sunspace R_p is complemented in M(p,w) if and only if it is isomorphic to l_2. However, the Rademacher subspace is not complemented in M(1,w) for any quasi-concave weight w. In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces M(p,w) is described. It turns out that for any infinite-dimensional subspace X of R_p the following alternative holds: either X is isomorphic to l_2 or X contains a subspace which is isomorphic to c_0 and is complemented in R_p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-23T05:07:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46B20",
      "46B42"
    ],
    "keywords": [
      "morrey spaces",
      "rademacher functions",
      "rademacher subspace",
      "isomorphic",
      "paper geometric structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150606862A"
    }
  }
}