Multiple singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces

This paper is devoted to studying the singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces, which contain many classical surfaces as model examples, on the product domains R-m x R-n (m, n >= 2). Under rather weak size conditions of the kernels, the L-p(R-m x R-n)-boundedness for such operators is established. These results essentially extend certain previous results.