{
  "id": "1607.06432",
  "version": "v1",
  "published": "2016-07-21T19:07:27.000Z",
  "updated": "2016-07-21T19:07:27.000Z",
  "title": "$A_1$ theory of weights for rough homogeneous singular integrals and commutators",
  "authors": [
    "C. Perez",
    "I. Rivera-Rios",
    "L. Roncal"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Quantitative $A_1-A_\\infty$ estimates for rough homogeneous singular integrals $T_{\\Omega}$ and commutators of $BMO$ symbols and $T_{\\Omega}$ are obtained. In particular the following estimates are proved: % \\[ \\|T_\\Omega \\|_{L^p(w)}\\le c_{n,p}\\|\\Omega\\|_{L^\\infty} [w]_{A_1}^{\\frac{1}{p}}\\,[w]_{A_{\\infty}}^{1+\\frac{1}{p'}}\\|f\\|_{L^p(w)} \\] % and % \\[ \\| [b,T_{\\Omega}]f\\|_{L^{p}(w)}\\leq c_{n,p}\\|b\\|_{BMO}\\|\\Omega\\|_{L^{\\infty}} [w]_{A_1}^{\\frac{1}{p}}[w]_{A_{\\infty}}^{2+\\frac{1}{p'}}\\|f\\|_{L^{p}\\left(w\\right)}, \\] % for $1<p<\\infty$ and $1/p+1/p'=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-21T19:07:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "rough homogeneous singular integrals",
      "commutators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}