{
  "id": "2108.00718",
  "version": "v1",
  "published": "2021-08-02T08:41:48.000Z",
  "updated": "2021-08-02T08:41:48.000Z",
  "title": "Composition operators on Besov and Triebel-Lizorkin spaces with power weights: necessary conditions",
  "authors": [
    "Douadi Drihem"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G:\\mathbb{R\\rightarrow R}$ be a continuous function. We investigate necessary conditions on $G$ such that \\begin{equation*} \\{G(f):f\\in A_{p,q}^{s}(\\mathbb{R}^{n},|\\cdot |^{\\alpha })\\}\\subset A_{p,q}^{s}(\\mathbb{R}^{n},|\\cdot |^{\\alpha }) \\end{equation*} holds. Here $A_{p,q}^{s}(\\mathbb{R}^{n},|\\cdot |^{\\alpha })$ stands for either the Besov space $B_{p,q}^{s}(\\mathbb{R}^{n},|\\cdot |^{\\alpha })$ or the Triebel-Lizorkin space $F_{p,q}^{s}(\\mathbb{R}^{n},|\\cdot |^{\\alpha })$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T08:41:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "47H30"
    ],
    "keywords": [
      "necessary conditions",
      "triebel-lizorkin space",
      "power weights",
      "composition operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}