{
  "id": "2210.03285",
  "version": "v1",
  "published": "2022-10-07T02:22:48.000Z",
  "updated": "2022-10-07T02:22:48.000Z",
  "title": "Improved Caffarelli-Kohn-Nirenberg Inequalities and Uncertainty Principle",
  "authors": [
    "Pei Dang",
    "Weixiong Mai"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on $\\mathbb R^n$, which is a further study of the results in \\cite{Dang-Deng-Qian}. Moreover, we also extend the extra-strong uncertainty principle given in \\cite{Dang-Qian-Chen} to cases for complex- and vector-valued functions defined on $\\mathbb S^n,n\\geq 2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-07T02:22:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "caffarelli-kohn-nirenberg inequalities",
      "extra-strong uncertainty principle",
      "vector-valued functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}