Inequalities of Carlson Type for $$\alpha $$-Bloch Functions

Abstract

In this article, we prove inequalities for the Taylor coefficients of functions G holomorphic in the unit disc satisfying the condition $$|G(z)|(1-|z|^2)^{\alpha }\le 1, |z|<1,$$ for fixed $$\alpha \ge 0.$$ 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 $$\alpha $$-Bloch functions and an estimate for an area type functional on $$\alpha $$-Bloch functions.