单位球上Bloch函数的带权特征

Weighted characterization of Bloch function in the unit ball of C^n

考虑 Cn 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( Bn) supλ∈ Bn‖ f .λ-f (λ)‖ p ,φ<∞ ,f∈ B0 ( Bn) lim|λ|→ 1 ‖ f .λ-f (λ)‖p ,φ=0 .

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) sup λ∈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.