A PROPERTY OF ANALYTIC-FUNCTIONS WITH HADAMARD GAPS

In this paper we obtain a sufficient and necessary condition for an analytic function f on D with Hadamard gaps, that is, for f(z) = [GRAPHICS] satisfying n(k + 1)/n(k) greater-than-or-equal-to lambda > 1 for all k, to belong to a kind of space consisting of analytic functions on D. The special cases of these spaces are B M O A and V M O A. In view of our result we can answer the open question given recently by Stroethoff.