{
  "id": "1001.1510",
  "version": "v2",
  "published": "2010-01-10T12:52:21.000Z",
  "updated": "2010-04-11T09:26:41.000Z",
  "title": "Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces and Their Applications",
  "authors": [
    "Wen Yuan",
    "Yoshihiro Sawano",
    "Dachun Yang"
  ],
  "comment": "30 pages, J. Math. Anal. Appl. (to appear).",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Let $p\\in(1,\\infty)$, $q\\in[1,\\infty)$, $s\\in\\mathbb{R}$ and $\\tau\\in[0, 1-\\frac{1}{\\max\\{p,q\\}}]$. In this paper, the authors establish the $\\varphi$-transform characterizations of Besov-Hausdorff spaces $B{\\dot H}_{p,q}^{s,\\tau}(\\mathbb{R}^n)$ and Triebel-Lizorkin-Hausdorff spaces $F{\\dot H}_{p,q}^{s,\\tau}(\\mathbb{R}^n)$ ($q>1$); as applications, the authors then establish their embedding properties (which on $B{\\dot H}_{p,q}^{s,\\tau}(\\mathbb{R}^n)$ is also sharp), smooth atomic and molecular decomposition characterizations for suitable $\\tau$. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in $B{\\dot H}_{p,q}^{s,\\tau}(\\mathbb{R}^n)$ and $F{\\dot H}_{p,q}^{s,\\tau}(\\mathbb{R}^n)$ ($q>1$), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when $p\\in(1,\\infty)$ and $q\\in[1,\\infty)$ by taking $\\tau=0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-11T09:26:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "42C40",
      "47G30"
    ],
    "keywords": [
      "triebel-lizorkin-hausdorff spaces",
      "molecular decomposition characterizations",
      "applications",
      "pseudo-differential operators",
      "besov-hausdorff spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}