Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces.

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case. [ABSTRACT FROM AUTHOR]