On the Sundberg approximation theorem

Abstract

Let H∞ be the Banach algebra of bounded holomorphic functions on the open unit disk D⊂C. We extend Sundberg's theorem on uniform approximation of functions in BMOA by H∞ functions to other classes of holomorphic functions on D. In our proofs we use a new characterization of meromorphic functions on D that extend to continuous maps of the maximal ideal space of H∞ to the Riemann sphere.