Abstract: In this paper, we consider a class of bounded Reinhardt domains D_α(m, n₁,…,n_m). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that D_α is a quasiconvex domain and D_α is a stronger quasiconvex domain if and only if D_α is a hypersphere.

Key words: bounded Reinhardt , domain;Cauchy-Szego , kernel