{
  "id": "math/0205007",
  "version": "v1",
  "published": "2002-05-01T11:42:26.000Z",
  "updated": "2002-05-01T11:42:26.000Z",
  "title": "Characterization of anysotropic Liouville-type mixed spaces and its application",
  "authors": [
    "V. A. Nogin",
    "E. E. Ournycheva"
  ],
  "comment": "LaTex, 23 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Within the framework of the method of hypersingular integrals we obtain a characterization of the anysotropic spaces $L_{\\bar p, \\bar r}^{\\bar \\alpha}$. These spaces are defined to consist of functions $f(x)\\in L_{\\bar r}$ for which $ F^{-1}(\\sum_{j=1}^n |\\xi_j|^{\\alpha_j})Ff\\in L_{\\bar p}, \\alpha_j>0. $ The mentioned characterization is applied to prove the denseness of the class $C_0^\\infty$ in $L_{\\bar p, \\bar r}^{\\bar \\alpha}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-01T11:42:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anysotropic liouville-type mixed spaces",
      "application",
      "anysotropic spaces",
      "hypersingular integrals",
      "mentioned characterization"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5007N"
    }
  }
}