关键词:  bounded symmetric domains, linear operator D^α,β weighted Bergman space A^p(Ω,dv_s), weighted Bergman space A^p_α,β(Ω,dv_s), duality

Abstract: On bounded symmetric domainΩof Cⁿ, we investigate the properties of functions in weighted Bergman spaces A^p(Ω,dv_s) for 0<p≤+∞ and -1<s<+∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^p(Ω,dv_s) in terms of a class of linear operators D^α,β. Making use of these characterizations, we ex- tend A^p(Ω,dv_s) to the weighted Berg-man spaces A^p_α,β(Ω,dv_s) in a very natural way for 1≤p≤+∞and any real number s, that is, -∞<s<+∞.This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on A^p_α,β(Ω,dv_s) and the dual of A^p_α,β(Ω,dv_s) are given. 

Key words:  bounded symmetric domains, linear operator D^α,β weighted Bergman space A^p(Ω,dv_s), weighted Bergman space A^p_α,β(Ω,dv_s), duality