【摘要】 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■的拟共形性质,对复伸张■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.更多还原

【Abstract】 We study the quasiconformal properties of the univalent harmonic functions ■ 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 ■. 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.更多还原