A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi

Abstract

In this paper, we study the higher-order Schwarzian derivative Sn (f) proposed by H. Tamanoi [Higher Schwarzian operators and combinatorics of the Schwarzian derivative, Math. Ann. 305 (1996), 127–151]. For the strongly starlike functions of order α and strongly convex functions of order α, the sharp bound of |S 3(f)(0)| is obtained. When n ∈ [2, 7], we prove that the higher Bers maps induced by Sn (f) on Weil-Petersson Teichmüller space and BMO-Teichmüller space are holomorphic.