On multiple singular integrals along polynomial curves with rough kernels

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the L ^p boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1 < p < ∞, are given. The research is supported by the NSF of China (Grant No. 10571122)