Boundedness of singular integral operators with variable kernels

Let K be a generalized Calderón–Zygmund kernel defined on Rn × (Rn \ {0}). The singular integral operator with variable kernel given by T f (x) = p.v. Rn K(x, x − y) f (y)dy is studied. We show that if the kernel K(x, y) satisfies the Lq-Hörmander condition with respect to x and y variables, respectively, then T is bounded on Lpw . If we add an extra Dini type condition on K, then we may show the Hpw − Lpw boundedness of T .