调和映射的Schwarz导数与对数导数的新定义及其范数

New definitions of Pre-Schwarzian and Schwarzian derivatives and its norm of harmonic mappings in the plan

借助能量密度|f_(z)|+t|f_(z)|,t∈[-1,1]对单连通区域上的局部单叶调和映射分别给出了Schwarz导数和对数导数的新定义,并在新定义下对它们的范数进行了研究。

With the help of energy density|f_(z)|+t|f_(z)|,t∈[-1,1],new definitions of Schwarz derivative and logarithmic derivative are given for the local unilobe harmonic mapping on a singly connected region,and their norms are studied under the new definition.