{
  "id": "2009.11650",
  "version": "v1",
  "published": "2020-09-24T13:09:05.000Z",
  "updated": "2020-09-24T13:09:05.000Z",
  "title": "An endpoint estimate for the commutators of singular integral operators with rough kernels",
  "authors": [
    "Guoen Hu",
    "Xiangxing Tao"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\Omega$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{d-1}$, $T_{\\Omega}$ be the homogeneous singular integral operator with kernel $\\frac{\\Omega(x)}{|x|^d}$ and $T_{\\Omega,\\,b}$ be the commutator of $T_{\\Omega}$ with symbol $b$. In this paper, we prove that if $\\Omega\\in L(\\log L)^2(S^{d-1})$, then for $b\\in {\\rm BMO}(\\mathbb{R}^d)$, $T_{\\Omega,\\,b}$ satisfies an endpoint estimate of $L\\log L$ type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-24T13:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "endpoint estimate",
      "rough kernels",
      "commutator",
      "mean value zero",
      "homogeneous singular integral operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}