P次对称典型实照函数的辐角估计

ARGUMENT ESTIMATION ABOUT d°(P) SYMMETRIC CANONICAL FUNCTION OF REAL SHINE

记单位圆内的P次对称正则典型实照函数族为T_r^((p))本文对P次对称正则典型实照函数fp(z)∈T_r^((p))进行了系统的研究,得到了关于argfp(z)和argfp(z)的精确估计。当P=1时就是戈鲁辛的结果。另外还对单位国外的正则典型实照函数F(ξ)∈∑r得到了关于argF(ξ)及argF′(ξ)的精确估计。

The family of d°(P) symmetric holomorphic canonical functions of real shine defined in a unit circle is denoted by T_r^(p). In this paper a systematic study of d°(P) symmetric holomrphic canonical function of real shine F_p(z)∈T_r^(p) is made and precise estimations about arg fp(z) and arg f′p(z) are obtained. When P=1, the estitmation is same as the Go Luzin result. Furthermore, the study of holomorphic canonical function of real shine F(§)∈∑_r outside the unit circle gives the exact estimaion on arg. F(§) and F′(§).