Vector-valued singular integral operators with non-smooth kernels and related multilinear commutators (Q938579)

Let \(({\mathcal X},d,\mu)\) be a space of homogeneous type. In this paper, the authors introduce the notion of vector-valued singular integrals \(T\) with non-smooth kernels on \({\mathcal X}\), and study the boundedness of \(T\) and its maximal truncated operator \(T_\ast\). Moreover, the authors introduce the notion of multilinear commutators generated by \(T\) and \(BMO\) functions or by \(T\) and Lipschitz functions, and establish the boundedness of these multilinear commutators.