{
  "id": "0908.4380",
  "version": "v2",
  "published": "2009-08-31T19:59:26.000Z",
  "updated": "2009-08-31T23:35:20.000Z",
  "title": "Littlewood-Paley characterization for $Q_α(R^n)$ spaces",
  "authors": [
    "Qifan Li"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In Baraka's paper [2], he obtained the Littlewood-Paley characterization of Campanato spaces $L^{2,\\lambda}$ and introduced $\\mathcal {L}^{p,\\lambda,s}$ spaces. He showed that $\\mathcal {L}^{2,\\lambda,s}=(-\\triangle)^{-\\frac{s}{2}}L^{2,\\lambda}$ for $0\\leq\\lambda<n+2$. In [7], by using the properties of fractional Carleson measures, J Xiao proved that for $n\\geq2$, $0<\\alpha<1$. $(-\\triangle)^{-\\frac{\\alpha}{2}}L^{2,n-2\\alpha}$ is essential the $Q_{\\alpha}(\\mathbb{R}^n)$ spaces which were introduced in [4]. Then we could conclude that $Q_{\\alpha}(\\mathbb{R}^n)=\\mathcal {L}^{2,n-2\\alpha,\\alpha}$ for $0<\\alpha<1$. In fact, this result could be also obtained directly by using the method in [2]. In this paper, We proved this result in the spirit of [2]. This paper could be considered as the supplement of Baraka's work [2].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-31T23:35:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25"
    ],
    "keywords": [
      "littlewood-paley characterization",
      "fractional carleson measures",
      "barakas paper",
      "barakas work",
      "campanato spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.4380L"
    }
  }
}