Canadian Journal of Pure & Applied Sciences

Abstract: In this paper we will generalize theorem 9 of Hahn and Mitchell (1969) in bounded symmetric domain on Hardy Space to Bergman Space. 1. Definition and Preliminary Results. Let D be a bounded symmetric domain in the complex vector space CN(N>1) in the cananical Harisch Chandra realization. It is known that D is circular and star-shaped with respect to 0?D and has a Bergman- Silov boundary b, which is circular and measurable. Let ? be the group of holomorphic automorphisms of D and 0 ? its isotropy subgroup with respect to 0. The group ? is transitive on D and the holomorphic automorphisms extend continuous to the topological boundary of D. The group 0 ? is transitive on b and b has a unique normalization 0 ? invariant measure ? which is given by 1 t t d? =V?ds, V the Euclidean volume of b and t ds the Euclidean volume element at t (Koranyi and Wolf, 1965). et H(D) denotes the class of holomorphic functions on as Ap(0