{
  "id": "2105.03717",
  "version": "v1",
  "published": "2021-05-08T15:21:15.000Z",
  "updated": "2021-05-08T15:21:15.000Z",
  "title": "Boundedness of operators generated by fractional semigroups associated with Schrödinger operators on Campanato type spaces via $T1$ theorem",
  "authors": [
    "Zhiyong Wang",
    "Pengtao Li",
    "Chao Zhang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\mathcal{L}=-\\Delta+V$ be a Schr\\\"{o}dinger operator, where the nonnegative potential $V$ belongs to the reverse H\\\"{o}lder class $B_{q}$. By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, $\\{e^{-t\\mathcal{L}^{\\alpha}}\\}_{t>0},$ associated with $\\mathcal{L}$. As an application, we obtain the $BMO^{\\gamma}_{\\mathcal{L}}$-boundedness of the maximal function, and the Littlewood-Paley $g$-functions associated with $\\mathcal{L}$ via $T1$ theorem, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-08T15:21:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B30",
      "35J10"
    ],
    "keywords": [
      "campanato type spaces",
      "schrödinger operators",
      "fractional semigroups",
      "boundedness",
      "fractional heat semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}