On rough singular integrals along real-analytic submanifolds

Abstract

Abstract Under some pretty much weaker size conditions assumed on the integral kernels both on the unit sphere and in the radial directions, the L p {L^{p}} boundedness was given for the rough singular integrals defined by translates of a real-analytic submanifold in ℝ n {\mathbb{R}^{n}} . Certain L p {L^{p}} estimates for the corresponding maximal rough singular integrals were also established.