WEIGHTED LP-BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACES

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Omega by assuming h is an element of Delta(gamma) (R+) and Omega is an element of WG(beta) (Sn-1) for some gamma > 1 and beta > 1. Here Omega is an element of WG(beta) (Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.