{
  "id": "1601.07615",
  "version": "v1",
  "published": "2016-01-28T01:29:17.000Z",
  "updated": "2016-01-28T01:29:17.000Z",
  "title": "Maximal Function Characterizations of Variable Hardy Spaces Associated with Non-negative Self-adjoint Operators Satisfying Gaussian Estimates",
  "authors": [
    "Ciqiang Zhuo",
    "Dachun Yang"
  ],
  "comment": "32 pages, submitted. arXiv admin note: text overlap with arXiv:1512.05950",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "Let $p(\\cdot):\\ \\mathbb R^n\\to(0,1]$ be a variable exponent function satisfying the globally $\\log$-H\\\"older continuous condition and $L$ a non-negative self-adjoint operator on $L^2(\\mathbb R^n)$ whose heat kernels satisfying the Gaussian upper bound estimates. Let $H_L^{p(\\cdot)}(\\mathbb R^n)$ be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels $\\{e^{-t^2L}\\}_{t\\in (0,\\infty)}$. In this article, the authors first establish the atomic characterization of $H_L^{p(\\cdot)}(\\mathbb R^n)$; using this, the authors then obtain its non-tangential maximal function characterization which, when $p(\\cdot)$ is a constant in $(0,1]$, coincides with a recent result by Song and Yan [Adv. Math. 287 (2016), 463-484] and further induces the radial maximal function characterization of $H_L^{p(\\cdot)}(\\mathbb R^n)$ under an additional assumption that the heat kernels of $L$ have the H\\\"older regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-28T01:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B25",
      "42B30",
      "42B35",
      "35K08"
    ],
    "keywords": [
      "self-adjoint operators satisfying gaussian estimates",
      "maximal function characterization",
      "non-negative self-adjoint operators satisfying gaussian",
      "variable hardy spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160107615Z"
    }
  }
}