Parabolic singular integrals with rough kernels and extrapolation

Abstract

This paper is devoted to studying the parabolic singular integrals with rough kernels both on the unit sphere and in the radial direction, as well as the corresponding maximal singular integrals. By the estimates of Fourier transforms, the Littlewood-Paley theory and the extrapolation arguments, under the rather weak size conditions, which are the best known ones so far, the L p bounds for such operators are established. As applications, the corresponding results for the corresponding operators associated to certain smooth surfaces are also obtained.