Area integrals for Riesz measures on the Siegel upper half space of type II (Q1802560)

This paper contains a proof of an important inequality comparing integrals of Riesz measures of subharmonic functions with integrals of their admissible maximal functions on the Siegel upper half-space of type II, which is identified by a coordinate change with \((0,\infty)\times H^ n\), where \(H^ n\) is the Heisenberg group. The inequality is an analogue of one obtained by \textit{T. R. McConnel} [Indiana Univ. Math. J. 33, 289-303 (1984; Zbl 0508.31005)] for the Euclidean upper half-space. The proof depends upon ingenious modification of previous results. Cf. \textit{M. Kaneko} [Tohoku Math. J., II. Ser. 39, 589-596 (1987; Zbl 0653.31003)].