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

Abstract

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 WFβ(Sn-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.