{
  "id": "1808.08227",
  "version": "v1",
  "published": "2018-08-24T17:51:50.000Z",
  "updated": "2018-08-24T17:51:50.000Z",
  "title": "Caffarelli-Kohn-Nirenberg inequalities on Besov and Triebel-Lizorkin-type spaces",
  "authors": [
    "Douadi Drihem"
  ],
  "comment": "24 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We present some Caffarelli-Kohn-Nirenberg-type inequalities on Herz-type Besov-Triebel-Lizorkin spaces. More Precisely, we investigate the inequalities \\begin{equation*} \\big\\|f\\big\\|_{\\dot{k}_{v,\\sigma}^{\\alpha _1,r}} \\leq c\\big\\|f\\big\\|_{\\dot{K}_u^{\\alpha _2,\\delta}}^{1-\\theta } \\big\\|f\\big\\|_{\\dot{K}_p^{\\alpha_3,\\delta _1} A_{\\beta }^s}^\\theta, \\end{equation*} with some appropriate assumptions on the parameters, where $\\dot{k}_{v,\\sigma }^{\\alpha _{1},r}$ is the Herz-type Bessel potential spaces. To do these, we study when distributions belonging to these spaces can be interpreted as functions in $L_{\\mathrm{loc}}^{1}$. Our main tools is the usual Littlewood-Paley technique, Sobolev and Franke embeddings, and interpolation theory. Our results improve their results in some sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-24T17:51:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B70",
      "46E35"
    ],
    "keywords": [
      "triebel-lizorkin-type spaces",
      "caffarelli-kohn-nirenberg inequalities",
      "herz-type bessel potential spaces",
      "usual littlewood-paley technique",
      "herz-type besov-triebel-lizorkin spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}