{
  "id": "2002.03136",
  "version": "v1",
  "published": "2020-02-08T10:38:53.000Z",
  "updated": "2020-02-08T10:38:53.000Z",
  "title": "Nuclear embeddings in weighted function spaces",
  "authors": [
    "Dorothee D. Haroske",
    "Leszek Skrzypczak"
  ],
  "comment": "2 figures",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We study nuclear embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results [17,19] where we studied the compactness of corresponding embeddings. The concept of nuclearity goes back to Grothendieck who defined it in [14]. Recently there is a refreshed interest to study such questions [5-8,49]. This led us to the investigation in the weighted setting. We obtain complete characterisations for the nuclearity of the corresponding embedding. Essential tools are a discretisation in terms of wavelet bases, operator ideal techniques, as well as a very useful result of Tong [43] about the nuclearity of diagonal operators acting in $\\ell_p$ spaces. In that way we can further contribute to the characterisation of nuclear embeddings on domains obtained in [5,33,34,49].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-08T10:38:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "47B10"
    ],
    "keywords": [
      "weighted function spaces",
      "operator ideal techniques",
      "nuclearity",
      "study nuclear embeddings",
      "weight belongs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}