Bulletin of the
Korean Mathematical Society BKMS

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 $T_qf(x)=\big(\sum_{k=1}^{\infty}|Tf_k(x)|^q\big)^{1/q}$. 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.

Keywords: weighted bound, singular integral operator, nonsmooth kernel, sparse operator, sharp maximal operator

MSC numbers: 42B20