{
  "id": "1903.08393",
  "version": "v1",
  "published": "2019-03-20T09:01:09.000Z",
  "updated": "2019-03-20T09:01:09.000Z",
  "title": "Littlewood-Paley Characterization for Musielak-Orlicz-Hardy Spaces Associated with Operators",
  "authors": [
    "Jiawei Shen",
    "Zhitian Chen",
    "Shunchao Long"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\\left(X\\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In this paper, the authors introduce a new characterization of the Musielak-Orlicz-Hardy Space $H_{\\varphi, L}\\left(X\\right)$ associated with $L$ in terms of the Lusin area function where $\\varphi$ is a growth function. Further, the authors prove that the Musielak-Orlicz-Hardy Space $H_{L,G,\\varphi}\\left(X\\right)$ associated with $L$ in terms of the Littlewood-Paley function is coincide with $H_{\\varphi, L}\\left(X\\right)$ and their norms are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-20T09:01:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B30",
      "42B35",
      "46E30",
      "47B38"
    ],
    "keywords": [
      "musielak-orlicz-hardy space",
      "littlewood-paley characterization",
      "gaussian upper bound",
      "non-negative second-order self-adjoint operator",
      "lusin area function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}