Area integrals for riesz measures on the siegel upper half space of type II

The area integrals of harmonic functions on the Siegel upper half space of type Ii are important tools for studying Hardy spaces and boundary behavior of harmonic functions. In this paper we will extend the area integrals to subharmonic functions on the Siegel upper half space of type Ii, and prove their Lp-estimates by the admissible maximal functions for all 0 <p <∞. The extended area integrals are analogues of the area integrals which were introduced by T. Mcconell in the case of the Euclidean upper half space.