A rough multiple Marcinkiewicz integral along continuous surfaces

By means of the method of block decompositions for kernel functions and some delicate estimates on Fourier transforms, the L-P (R-m x R-n x R)-boundedness of the multiple Marcinkiewicz integral is established along a continuous surface with rough kernel for some p > 1. The condition on the integral kernel is the best possible for the L-2-boundedness of the multiple Marcinkiewicz integral operator