{
  "id": "2406.18527",
  "version": "v1",
  "published": "2024-06-26T17:56:04.000Z",
  "updated": "2024-06-26T17:56:04.000Z",
  "title": "Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces",
  "authors": [
    "Ryan Alvarado",
    "Przemysław Górka",
    "Artur Słabuszewski"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the setting of quasi-metric spaces, the main results in this article are new, even in the metric setting. Moreover, by considering the more general category of quasi-metric spaces we are able to obtain these characterizations for optimal ranges of exponents that depend (quantitatively) on the geometric makeup of the underlying space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-26T17:56:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triebel-lizorkin spaces",
      "compact embeddings",
      "quasi-metric spaces",
      "sufficient conditions guaranteeing compactness",
      "fractional sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}