单位球上Bloch函数的带权特征

摘要

考虑C+n中单位球上的Bloch函数和小Bloch函数，利用正规函数φ的性质，给出了Bloch的带权特征，即：f∈B(B-n)supλ∈B-n‖fφ-λ-f(λ)‖-{p,φ}<∞,f∈B-0(B-n)lim|λ|→1‖fφ-λ-f(λ)‖-{p,φ}=0.推广了单位圆盘上的相应结果.%The Bloch space and little Bloch space in the unit ball were studied.In this condition of weighted measure with normal function φ,the author obtained the equivalence of Bloch function and little Bloch function: f∈B(B-n)supλ∈B-n‖fφ-λ-f(λ)‖-{p,φ}<∞,f∈B-0(B-n)lim|λ|→1‖fφ-λ-f(λ)‖-{p,φ}=0.Which was a generalization of the result in the unit disc.