一类单叶调和函数的拟共形性质

研究单位圆盘D={z||z|<1}上满足Re{αz［h″(z)+g″(z)］+h’(z)+g’(z)}>0,z∈D,α>0的单叶调和函数f(z)=h(z)+g(z)^-的拟共形性质,对复伸张w(z)=(g’(z))/(h’(z))的模给出最好的最小上界估计,进而给出该类函数到D的余集D^c上的拟共形延拓,并对其复伸张的模给出最好的最小上界估计,改进和推广了2004年Yalcin S等的研究成果.

On Quasiconformal Properties for One Set of Univalent Harmonic Mappings

We study the quasiconformal properties of the univalent harmonic functions f(z)=h(z)+g(z)^- on the unit disk D={z||z|<1} with Re{αz［h″(z)+g″(z)］+h’(z)+g’(z)}>0, z∈D, α>0, and obtain the best upper bound estimation for the module of the dilatation function w(z)=(g’(z))/(h’(z)). Moreover, we construct their harmonic quasiconformal extension functions to the domain D^c of D, and give the best upper bound estimation for the module of their dilatation functions. The results improve and generalize the ones made by Yalcin S, et al in 2004.