论文标题
Schwarzian规范估计某些类别的分析功能
Schwarzian norm estimates for some classes of analytic functions
论文作者
论文摘要
令$ \ MATHCAL {A} $表示单位磁盘$ \ Mathbb {d} = \ {z \ in \ Mathbb {C}：| | z | <1 \} $由$ f（0）= 0 $，$ f'（0）= 1 $正常化。在本文中，我们获得了Schwarzian规范$ \ Mathcal {g}（β）= \ {f \ in \ Mathcal {a}：{\ rm re \，} [1+zf'（z）/f'（z）/f'（z）/f'（z）] <1+β/2+β$，在$ MATHCAL {a a}中获得施加兹的尖锐估计。 $ \ MATHCAL {f}（α）= \ {f \ in \ Mathcal {a}：{\ rm re \，} [1+zf''（z）/f'（z）/f'（z）>α\} $，其中$ -1/2 \ leleα\ le le 0 $。我们还为$ \ mathcal {g}（β）$和$ \ Mathcal {f}（α）$的类中的功能建立了两点失真定理。
Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. In the present article, we obtain the sharp estimates of the Schwarzian norm for functions in the classes $\mathcal{G}(β)=\{f\in \mathcal{A}:{\rm Re\,}[1+zf''(z)/f'(z)]<1+β/2\}$, where $β>0$ and $\mathcal{F}(α)=\{f\in \mathcal{A}:{\rm Re\,}[1+zf''(z)/f'(z)]>α\}$, where $-1/2\le α\le 0$. We also establish two-point distortion theorem for functions in the classes $\mathcal{G}(β)$ and $\mathcal{F}(α)$.
