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QUANTITATIVE WEIGHTED BOUNDS FOR THE VECTOR-VALUED SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS

  • Hu, Guoen (School of Applied Mathematics Beijing Normal University)
  • Received : 2017.12.12
  • Accepted : 2018.05.03
  • Published : 2018.11.30

Abstract

Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

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