NOTE ON THE SPACE BMOA

Let D be the unit disc in the complex plane. It is shown that (i) for 0 < p < 2, there exists an analytic function f is-an-element-of BMOA for which integral D[f'(z)[p(1 - Absolute value of z 2)p-2(1 - [phi(a)(z)[2) dx dy = infinity when Absolute value of a < 1, and (ii) for 2 < p < infinity, there exists an analytic function f is-not-an-element-of BMOA for which [GRAPHICS] This settles the question of Stroethoff [5] on BMOA.