SHARP DISTORTION ESTIMATE FOR LOCALLY SCHLICHT BLOCH FUNCTIONS

Let B-infinity be the space of locally schlicht Bloch functions f which are analytic in the unit disc Delta with f(0) = f'(0)-1 = 0 satisfying 0 < /f'(z)/(1-/z/(2)) less than or equal to 1 For each fixed z(0) is an element of Delta we shall determine the shape of the set (logf'(z(0)):f is an element of B-infinity}, that is, we shall give the sharp distortion estimate for locally schlicht Bloch functions.