{
  "id": "1901.05600",
  "version": "v1",
  "published": "2019-01-17T03:14:52.000Z",
  "updated": "2019-01-17T03:14:52.000Z",
  "title": "Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces",
  "authors": [
    "Fan Wang",
    "Dachun Yang",
    "Sibei Yang"
  ],
  "comment": "46 pages; Submitted",
  "categories": [
    "math.CA",
    "math.AP",
    "math.FA"
  ],
  "abstract": "Let $X$ be a ball quasi-Banach function space and $H_X(\\mathbb{R}^n)$ the associated Hardy-type space. In this article, the authors establish the characterizations of $H_X(\\mathbb{R}^n)$ via the Littlewood-Paley $g$-functions and $g_\\lambda^\\ast$-functions. Moreover, the authors obtain the boundedness of Calder\\'on-Zygmund operators on $H_X(\\mathbb{R}^n)$. For the local Hardy-type space $h_X(\\mathbb{R}^n)$, the authors also obtain the boundedness of $S^0_{1,0}(\\mathbb{R}^n)$ pseudo-differential operators on $h_X(\\mathbb{R}^n)$ via first establishing the atomic characterization of $h_X(\\mathbb{R}^n)$. Furthermore, the characterizations of $h_X(\\mathbb{R}^n)$ by means of local molecules and local Littlewood-Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz-Hardy space, the Lorentz-Hardy space, the Morrey-Hardy space, the variable Hardy space, the Orlicz-slice Hardy space and their local versions. Some special cases of these applications are even new and, particularly, in the case of the variable Hardy space, the $g_\\lambda^\\ast$-function characterization obtained in this article improves the known results via widening the range of $\\lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-17T03:14:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "42B35",
      "42B25",
      "46E30"
    ],
    "keywords": [
      "ball quasi-banach function space",
      "variable hardy space",
      "applications",
      "characterization",
      "local hardy-type space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}