{
  "id": "2001.02046",
  "version": "v1",
  "published": "2020-01-07T14:19:46.000Z",
  "updated": "2020-01-07T14:19:46.000Z",
  "title": "Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains",
  "authors": [
    "Helena F. Gonçalves",
    "Dorothee D. Haroske",
    "Leszek Skrzypczak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_\\tau : {B}_{p_1,q_1}^{s_1,\\tau_1}(\\Omega) \\hookrightarrow {B}_{p_2,q_2}^{s_2,\\tau_2}(\\Omega)$ and $id_\\tau : {F}_{p_1,q_1}^{s_1,\\tau_1}(\\Omega) \\hookrightarrow {F}_{p_2,q_2}^{s_2,\\tau_2}(\\Omega) $, where $\\Omega \\subset {\\mathbb R}^d$ is a bounded domain, and obtain necessary and sufficient conditions for the compactness of $id_\\tau$. Moreover, we characterise its entropy and approximation numbers. Surprisingly, these results are completely obtained via embeddings and the application of the corresponding results for classical Besov and Triebel-Lizorkin spaces as well as for Besov-Morrey and Triebel-Lizorkin-Morrey spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-07T14:19:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triebel-lizorkin-type spaces",
      "bounded domain",
      "compact embeddings",
      "besov-type",
      "triebel-lizorkin-morrey spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}