Boundedness of singular integral operators with variable kernels

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