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).
基金
the1 5 1 Projection and the Natural Science Foundation of Zhejiang Province( M1 0 31 0 4 )
