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This paper is devoted to studying the singular integral operators associated to polynomial mappings as well as the corresponding compound sub-manifolds. 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.

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