【摘要】 记DC为单位圆盘,B^k C^k为开欧氏单位球,Ω是C^k（或C）中的域.记H_n（D,Ω）为满足一定条件的全纯映照族（或函数族）的全体.作者证明了若,∈Hn（D,D）,则|f′（z）|≤(n|z|^n-1)/(1-|z|²ⁿ)(1-|f|（z|²）,z∈DD同时,对Hn（D,B^k）中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果.更多还原

【Abstract】 Let D be the unit disk in C,B^k be the Euclidean unit ball in C^k,Ω is a domain in C^k（or C）.Let H_n（D,Ω） be the set of all holomorphic mappings / from D into Ω which satisfies a certain condition.In this paper,it is proved that if f∈H_n（D,D）,then|f′（z）|≤(n|z|^n-1)/(1-|z|²ⁿ)(1-|f|（z|²）,z∈D.Meanwhile,we obtain a similar result for the modulus of mappings in H_n（B,B^k）.The result generalizes the corresponding result obtained earlier by Pavlovic.更多还原