{
  "id": "2302.00811",
  "version": "v1",
  "published": "2023-02-02T00:57:38.000Z",
  "updated": "2023-02-02T00:57:38.000Z",
  "title": "Boundedness of composition operators on higher order Besov spaces in one dimension",
  "authors": [
    "Masahiro Ikeda",
    "Isao Ishikawa",
    "Koichi Taniguchi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper aims to characterize boundedness of composition operators on Besov spaces $B^s_{p,q}$ of higher order derivatives $s>1+1/p$ on the one-dimensional Euclidean space. In contrast to the lower order case $0<s<1$, there were a few results on the boundedness of composition operators for $s>1$. We prove a relation between the composition operators and pointwise multipliers of Besov spaces, and effectively use the characterizations of the pointwise multipliers. As a result, we obtain necessary and sufficient conditions for the boundedness of composition operators for general $p$, $q$, and $s$ such that $1<p\\le \\infty$, $0<q\\le \\infty$, and $s>1+1/p$. In this paper, we treat, as a map that induces the composition operator, not only a homeomorphism on the real line but also a continuous map whose number of elements of inverse images at any one point is bounded above. We also show a similar characterization of the boundedness of composition operators on Triebel-Lizorkin spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-02T00:57:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "30H25",
      "46E35"
    ],
    "keywords": [
      "composition operator",
      "higher order besov spaces",
      "boundedness",
      "higher order derivatives",
      "one-dimensional euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}