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

Abstract

. In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ (cid:52) γ ( R + ) and Ω ∈ WG β (S n − 1 ) for some γ > 1 and β > 1. Here Ω ∈ WG β (S n − 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.