The Derivative of a Bounded Holomorphic Function in the Disk
The Derivative of a Bounded Holomorphic Function in the Disk
Let a nonconstant function / be holomorphic and bounded, l/l <1 in D: |z|<l.We shall estimate f*(z)=(l-|z|2)|/'(z)|/(l -|/(z)|2) at each point z e D ((1) in Theorem 1).The function d appearing in the estimate concerns the sizes of the schlicht disks on the Riemannian image J of D by /.Boundary …