Equivalent Characterizations of μ-Bloch Functions on the Unit Ball in Cn

摘要

Let μ be a normal function on [0,1）. In this paper, the authors give some equivalent characterizations of μ-Bloch functions on the unit ball in Cn. They prove that the following conditions are equivalent: (2) f ? H(B) and the function μ(|z|)(l- |z|~2)~(r-1) R~(α,r) f(z） is bounded in B; (3) f ? H(B) and the function μ |z|~2)~(M_1-1)(δ~(M_1)/δ_z~m(z） is bounded in B,where |m| ニ M_1; (4) f e H(B) and the function μ(|z|)(1 - |z|~2)~(M_2-1) R~((M_2)) f(z） is bounded in B.