WEIGHTED INTEGRALS OF HOLOMORPHIC FUNCTIONS  

作　　者：HuZhangjian LiuTaishun 

机构地区：[1]Dept.ofMath.,Univ.ofSci.andTech.ofChina,Hefei230026,China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2004年第4期474-480,共7页高校应用数学学报（英文版）（B辑）

基　　金：the1 5 1 Projection and the Natural Science Foundation of Zhejiang Province( M1 0 31 0 4 )

摘　　要：Given an admissible weight w and 0<p<∞, the estimate∫ D|f(z)| pw(z)dm(z)～|f(0)| p+∫ D|f′(z)| p ψ p(z)w(z)dm(z)is valid for all holomorphic functions f in the unit disc D. Here,ψ(r)=∫ 1 rw(t)dtw(r) is the distortion of w. As an application of the above estimate, it is proved that the Cesàro operator C[·] is bounded on the weighted Bergman spaces L p a,w (D).Given an admissible weight w and 0<p<∞, the estimate∫ D|f(z)| pw(z)dm(z)～|f(0)| p+∫ D|f′(z)| p ψ p(z)w(z)dm(z)is valid for all holomorphic functions f in the unit disc D. Here,ψ(r)=∫ 1 rw(t)dtw(r) is the distortion of w. As an application of the above estimate, it is proved that the Cesàro operator C[·] is bounded on the weighted Bergman spaces L p a,w (D).

关 键 词：admissible weight holomorphic functions Cesàro operator. 

分 类 号：O177.2[理学—数学]