{
  "id": "2404.05813",
  "version": "v1",
  "published": "2024-04-08T18:27:59.000Z",
  "updated": "2024-04-08T18:27:59.000Z",
  "title": "A linear operator bounded in all Besov but not in Triebel-Lizorkin spaces",
  "authors": [
    "Liding Yao"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We construct a linear operator $T:\\mathscr S'(\\mathbb R^n)\\to \\mathscr S'(\\mathbb R^n)$ such that $T:\\mathscr B_{pq}^s(\\mathbb R^n)\\to\\mathscr B_{pq}^s(\\mathbb R^n)$ for all $0<p,q\\le\\infty$ and $s\\in\\mathbb R$, but $T(\\mathscr F_{pq}^s(\\mathbb R^n))\\not\\subset \\mathscr F_{pq}^s(\\mathbb R^n)$ unless $p=q$. As a result Triebel-Lizorkin spaces cannot be interpolated from Besov spaces unless $p=q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-08T18:27:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "42B35",
      "42B25"
    ],
    "keywords": [
      "linear operator",
      "result triebel-lizorkin spaces",
      "besov spaces unless"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}