{
  "id": "0903.4583",
  "version": "v2",
  "published": "2009-03-26T13:46:07.000Z",
  "updated": "2010-07-19T14:15:00.000Z",
  "title": "New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces",
  "authors": [
    "Dachun Yang",
    "Yuan Zhou"
  ],
  "comment": "Manuscripta Math., to appear",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "An RD-space $\\mathcal X$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\\mathcal X$. In this paper, the authors first give several equivalent characterizations of RD-spaces and show that the definitions of spaces of test functions on $\\mathcal X$ are independent of the choice of the regularity $\\epsilon\\in (0,1)$; as a result of this, the Besov and Triebel-Lizorkin spaces on $\\mathcal X$ are also independent of the choice of the underlying distribution space. Then the authors characterize the norms of inhomogeneous Besov and Triebel-Lizorkin spaces by the norms of homogeneous Besov and Triebel-Lizorkin spaces together with the norm of local Hardy spaces in the sense of Goldberg. Also, the authors obtain the sharp locally integrability of elements in Besov and Triebel-Lizorkin spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-19T14:15:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "42B30",
      "43A99"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "reverse doubling property holds",
      "local hardy spaces",
      "additional property",
      "sharp locally integrability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.4583Y"
    }
  }
}