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

Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and T-q(q is an element of (1, infinity)) be the vector-valued operator defined by T-q f(x) = ( Sigma(infinity)(k=1)vertical bar Tf-k(x)vertical bar(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.