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Let $T$ be a singular integral operator with non-smooth kernel which wereintroduced by Duong and McIntosh. In this paper, we prove that this operatorand its corresponding grand maximal operator satisfies certain weak typeendpoint vector-valued estimate of $L\log L$ type. As an application weestablished a refined weighted vector-valued bound for this operator.

Weighted vector-valued bounds for the singular integral operators with nonsmooth kernels