Hilbert integrals on Siegel domains of type II

The Šilov boundary of a Siegel domain of type II is equivalent to a 2-step nilpotent Lie group. In this paper, we mainly study the L^p-boundness of the Hilbert integrals on Siegel domains of type II by using F. Ricci and E.M. Stein's result about singular integrals on Lie groups^1]. This is the generalization of part of the work done by P.H.Phong and E.M.Stein in 2]