On a class of singular integral operators with rough kernels

In this paper, we study the L^p mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on L^p provided that their kernels satisfy a size condition much weaker than that for the classical Calderón-Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.