Estimates for Singular Integrals along Surfaces of Revolution

We prove certain L estimates (1 < p <∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain L boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals.