Far Eastern Mathematical Journal

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Two-point boundary distortion estimate for Schwarzian derivative of holomorphic function

V. N. Dubinin

2014, issue 2, P. 191–199

Abstract

Let $f$ be a holomorphic function in the disk $|z|<1$, $|f(z)|<1$, and let $z_1, z_2$ are distinct boundary points of this disk in which the angular limits $f(z_k), k=1,2$, exist, $f(z_{1})\neq f(z_{2})$, $|f(z_1)|=|f(z_2)|=1$. Under some geometric constraints on f the precise upper bound for $\Re\{S_{f}(z_{1})+S_{f}(z_{2})\}$ is established. Here $S_{f}(z)$ means the Schwarzian derivative of the function $f$ at the point $z$.

Keywords: Schwarzian derivative, holomorphic functions, boundary distortion

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References

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