{
  "id": "0909.2072",
  "version": "v2",
  "published": "2009-09-11T01:02:16.000Z",
  "updated": "2009-11-02T15:39:41.000Z",
  "title": "A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions",
  "authors": [
    "Pekka Koskela",
    "Dachun Yang",
    "Yuan Zhou"
  ],
  "comment": "J. Funct. Anal. (to appear)",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we establish the equivalence between the Haj{\\l}asz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when $p\\in(n/(n+1),\\infty)$, we give a new characterization of the Haj{\\l}asz-Sobolev spaces $\\dot M^{1, p}({\\mathbb R}^n)$ via a grand Littlewood-Paley function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-02T15:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B30",
      "46E35",
      "42B25"
    ],
    "keywords": [
      "grand littlewood-paley function",
      "characterization",
      "hajłasz-sobolev",
      "grand triebel-lizorkin spaces",
      "euclidean spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2072K"
    }
  }
}