{
  "id": "1004.5507",
  "version": "v1",
  "published": "2010-04-30T11:45:42.000Z",
  "updated": "2010-04-30T11:45:42.000Z",
  "title": "Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings",
  "authors": [
    "Pekka Koskela",
    "Dachun Yang",
    "Yuan Zhou"
  ],
  "journal": "Advance in Math. 226 (2011) 3579-3621",
  "categories": [
    "math.CA",
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\\dot B^s_{p,\\,q}$ and Triebel-Lizorkin spaces $\\dot F^s_{p,\\,q}$ for all $s\\in(0,\\,1)$ and $p,\\,q\\in(n/(n+s),\\,\\infty],$ both in ${\\mathbb R}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve $\\dot F^s_{n/s,\\,q}$ on $\\rn$ for all $s\\in(0,\\,1)$ and $q\\in(n/(n+s),\\,\\infty]$. A metric measure space version of the above morphism property is also established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-30T11:45:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C65",
      "42B35",
      "42B25",
      "46E35",
      "30L10"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "pointwise characterizations",
      "metric measure space version",
      "quasiconformal mappings preserve",
      "metric measure spaces enjoying"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.5507K"
    }
  }
}