ROUGH SINGULAR INTEGRALS SUPPORTED BY SUBMANIFOLDS IN TRIEBEL-LIZORKIN SPACES AND BESOVE SPACES

Abstract

This paper is devoted to studying the singular integral operators associated to polynomial mappings as well as the corresponding compound submanifolds. By imposing a restrictive condition on the kernels of the operators in the radial direction, the boundedness for such operators on Triebel-Lizorkin spaces and Besov spaces are established, provided that the kernels satisfy a rather weak size condition on the unit sphere, which is distinct from the Hardy space functions. Some previous results are essentially improved and generalized.