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

Abstract

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

13 pages, corrected the proof of Lemma 2.1, and corrected some misprints