Inequalities of Carlson Type for α -Bloch Functions

Abstract

© 2020, Springer Nature Switzerland AG. In this article, we prove inequalities for the Taylor coefficients of functions G holomorphic in the unit disc satisfying the condition | G(z) | (1 - | z| 2) α≤ 1 , | z| < 1 , for fixed α≥ 0. The upper bound for the modulus of the k-th Taylor coefficient is dependent on the moduli of some initial coefficients. As corollaries we get similar estimates for α-Bloch functions and an estimate for an area type functional on α-Bloch functions.