{
  "id": "1903.10265",
  "version": "v1",
  "published": "2019-03-25T12:15:23.000Z",
  "updated": "2019-03-25T12:15:23.000Z",
  "title": "Strict singularity of weighted composition operators on derivative Hardy spaces",
  "authors": [
    "Qingze Lin",
    "Junming Liu",
    "Yutian Wu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We prove that the weighted composition operator $W_{\\phi,\\varphi}$ fixes an isomorphic copy of $\\ell^p$ if the operator $W_{\\phi,\\varphi}$ is not compact on the derivative Hardy space $S^p$. In particular, this implies that the strict singularity of the operator $W_{\\phi,\\varphi}$ coincides with the compactness of it on $S^p$. Moreover, when $p\\neq2$, we characterize the conditions for those weighted composition operators $W_{\\phi,\\varphi}$ on $S^p$ which fix an isomorphic copy of $\\ell^2$ .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-25T12:15:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "30H05"
    ],
    "keywords": [
      "weighted composition operator",
      "derivative hardy space",
      "strict singularity",
      "isomorphic copy",
      "compactness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}