A property of analytic functions with Hadamard gaps

Abstract

In this paper we obtain a sufficient and necessary condition for an analytic function f on D with Hadamard gaps, that is, for satisfying n k+1 / n k ≥ λ 1 for all k , to belong to a kind of space consisting of analytic functions on D . The special cases of these spaces are BMOA and VMOA . In view of our result we can answer the open question given recently by Stroethoff.