{
  "id": "1201.1945",
  "version": "v4",
  "published": "2012-01-10T00:51:13.000Z",
  "updated": "2014-01-29T00:30:24.000Z",
  "title": "Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications",
  "authors": [
    "Shaoxiong Hou",
    "Dachun Yang",
    "Sibei Yang"
  ],
  "journal": "Commun. Contemp. Math. 15 (2013), no. 6, 1350029, 37 pp",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $\\varphi: \\mathbb R^n\\times [0,\\infty)\\to[0,\\infty)$ be a growth function such that $\\varphi(x,\\cdot)$ is nondecreasing, $\\varphi(x,0)=0$, $\\varphi(x,t)>0$ when $t>0$, $\\lim_{t\\to\\infty}\\varphi(x,t)=\\infty$, and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty(\\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_\\varphi(\\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the $\\varphi$-Carleson measure characterization of the Musielak-Orlicz ${\\mathop\\mathrm{BMO}}$-type space $\\mathop\\mathrm{BMO}_{\\varphi}(\\mathbb{R}^n)$, which was proved to be the dual space of $H_\\varphi(\\mathbb{R}^n)$ by Luong Dang Ky.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-01-29T00:30:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B30",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "musielak-orlicz hardy space",
      "lusin area function",
      "molecular characterizations",
      "luong dang ky",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1945H"
    }
  }
}