{
  "id": "math/0512315",
  "version": "v1",
  "published": "2005-12-14T10:08:51.000Z",
  "updated": "2005-12-14T10:08:51.000Z",
  "title": "Commutators of integral operators with variable kernels on Hardy spaces",
  "authors": [
    "Pu Zhang",
    "Kai Zhao"
  ],
  "comment": "12 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 399-410",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\T (0\\leq \\alpha <n)$ be the singular and fractional integrals with variable kernel $\\Omega(x,z)$, and $[b,\\T]$ be the commutator generated by $\\T$ and a Lipschitz function $b$. In this paper, the authors study the boundedness of $[b,\\T]$ on the Hardy spaces, under some assumptions such as the $L^r$-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators $\\tT (0\\leq \\alpha <n)$. The smoothness conditions imposed on $\\tOmega$ are weaker than the corresponding known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-14T10:08:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B30"
    ],
    "keywords": [
      "hardy spaces",
      "variable kernel",
      "integral operators",
      "commutator",
      "weak type estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12315Z"
    }
  }
}