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A systematic treatment is given of singular integrals and Marcinkiewicz integrals associated with surfaces generated by polynomial compound mappings as well as related maximal functions with rough kernels in  W    F    β    (    S    n  -  1    )  , which relates to the Grafakos-Stefanov function class. Certain boundedness and continuity for these operators on Triebel-Lizorkin spaces and Besov spaces are proved by applying some criterions of bounds and continuity for several operators on the above function spaces.

Boundedness and Continuity of Several Integral Operators with Rough Kernels inWFβSn-1on Triebel-Lizorkin Spaces