{
  "id": "1307.5466",
  "version": "v3",
  "published": "2013-07-20T21:32:17.000Z",
  "updated": "2017-01-10T13:24:55.000Z",
  "title": "Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces",
  "authors": [
    "António Caetano",
    "Amiran Gogatishvili",
    "Bohumír Opic"
  ],
  "comment": "24 pages",
  "journal": "Proceedings of the Royal Society of Edinburgh, Section A, Mathematics, 146 (2016), 905-927",
  "doi": "10.1017/S0308210515000761",
  "categories": [
    "math.FA"
  ],
  "abstract": "There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\\mathbb R^n)$, $1 \\leq p < \\infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\\mathbb R^n)$, $0<s<1$, $0<p,q\\leq \\infty$, into Lorentz-type spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-07T15:09:41.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-01-10T13:24:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46E35",
      "46B42",
      "46B50"
    ],
    "keywords": [
      "besov-type spaces",
      "applications",
      "power quasi-banach function spaces",
      "abstract besov spaces",
      "main aims"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5466C"
    }
  }
}