{
  "id": "2502.01095",
  "version": "v1",
  "published": "2025-02-03T06:34:37.000Z",
  "updated": "2025-02-03T06:34:37.000Z",
  "title": "On subordinated semigroups and Hardy spaces associated to fractional powers of operators",
  "authors": [
    "The Anh Bui",
    "Michael G. Cowling",
    "Xuan Thinh Duong"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $L$ be a positive self-adjoint operator on $L^2(X)$, where $X$ is a $\\sigma$-finite metric measure space. When $\\alpha \\in (0,1)$, the subordinated semigroup $\\{\\exp(-tL^{\\alpha}):t \\in \\mathbb{R}^+\\}$ can be defined on $L^2(X)$ and extended to $L^p(X)$. We prove various results about the semigroup $\\{\\exp(-tL^{\\alpha}):t \\in \\mathbb{R}^+\\}$, under different assumptions on $L$. These include the weak type $(1,1)$ boundedness of the maximal operator $f \\mapsto \\sup _{t\\in \\mathbb{R}^+}\\exp(-tL^{\\alpha})f$ and characterisations of Hardy spaces associated to the operator $L$ by the area integral and vertical square function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-03T06:34:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B30",
      "42B35"
    ],
    "keywords": [
      "hardy spaces",
      "subordinated semigroup",
      "fractional powers",
      "finite metric measure space",
      "positive self-adjoint operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}