Weighted Bergman Spaces on Bounded Symmetric Domains  

有界对称域上的加权Bergman空间(英文)

作　　者：王雄亮 刘太顺 

机构地区：[1]Department of Mathematics,University of Science and Technology of China [2]Department of Mathematics,Huzhou Teacher's College

出　　处：《Chinese Quarterly Journal of Mathematics》2008年第1期36-44,共9页数学季刊（英文版）

基　　金：the NNSF of China(10571164);the SRFDP of Higher Education(20050358052)

摘　　要：On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ 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 Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.

关 键 词：bounded symmetric domains linear operator D^αB weighted Bergman space A^P （ Ω  dvs） weighted Bergman space Aα^p β （Ω  dvs ） DUALITY 

分 类 号：O174.56[理学—数学]