{
  "id": "1603.04927",
  "version": "v1",
  "published": "2016-03-16T00:56:28.000Z",
  "updated": "2016-03-16T00:56:28.000Z",
  "title": "Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian Estimates",
  "authors": [
    "Dachun Yang",
    "Sibei Yang"
  ],
  "comment": "28 pages; Submitted",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Let $L$ be a non-negative self-adjoint operator on $L^2(\\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\\varphi:\\,\\mathbb{R}^n\\times[0,\\infty) \\to[0,\\infty)$ satisfies that $\\varphi(x,\\cdot)$ is an Orlicz function and $\\varphi(\\cdot,t)\\in {\\mathbb A}_{\\infty}(\\mathbb{R}^n)$ (the class of uniformly Muckenhoupt weights). Let $H_{\\varphi,\\,L}(\\mathbb{R}^n)$ be the Musielak-Orlicz-Hardy space introduced via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors obtain several maximal function characterizations of the space $H_{\\varphi,\\,L}(\\mathbb{R}^n)$, which, especially, answer an open question of L. Song and L. Yan under an additional mild assumption satisfied by Schr\\\"odinger operators on $\\mathbb{R}^n$ with non-negative potentials belonging to the reverse H\\\"older class, and second-order divergence form elliptic operators on $\\mathbb{R}^n$ with bounded measurable real coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-16T00:56:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "self-adjoint operators satisfying gaussian estimates",
      "non-negative self-adjoint operators satisfying gaussian",
      "maximal function characterizations",
      "musielak-orlicz-hardy space",
      "divergence form elliptic operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}