{
  "id": "1201.4062",
  "version": "v4",
  "published": "2012-01-19T14:06:45.000Z",
  "updated": "2012-05-24T03:26:50.000Z",
  "title": "New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces",
  "authors": [
    "Yiyu Liang",
    "Jizheng Huang",
    "Dachun Yang"
  ],
  "comment": "J. Math. Anal. Appl. (to appear)",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Let $\\varphi: {\\mathbb R^n}\\times [0,\\infty)\\to[0,\\infty)$ be such that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)$ is a Muckenhoupt $A_\\infty({\\mathbb R^n})$ weight. The Musielak-Orlicz Hardy space $H^{\\varphi}(\\mathbb R^n)$ is defined to be the space of all $f\\in{\\mathcal S}'({\\mathbb R^n})$ such that the grand maximal function $f^*$ belongs to the Musielak-Orlicz space $L^\\varphi(\\mathbb R^n)$. Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of $H^{\\varphi}(\\mathbb R^n)$ in terms of the vertical or the non-tangential maximal functions, or the Littlewood-Paley $g$-function or $g_\\lambda^\\ast$-function, via first establishing a Musielak-Orlicz Fefferman-Stein vector-valued inequality. Moreover, the range of $\\lambda$ in the $g_\\lambda^\\ast$-function characterization of $H^\\varphi(\\mathbb R^n)$ coincides with the known best results, when $H^\\varphi(\\mathbb R^n)$ is the classical Hardy space $H^p(\\mathbb R^n)$, with $p\\in (0,1]$, or its weighted variant.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-05-24T03:26:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B30",
      "42B35"
    ],
    "keywords": [
      "musielak-orlicz hardy space",
      "real-variable characterizations",
      "grand maximal function",
      "non-tangential maximal functions",
      "musielak-orlicz fefferman-stein vector-valued inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4062L"
    }
  }
}