  Let D be a bounded domain in the complex plane whose boundary consists of m
pairwise disjoint simple closed curves where m is greater than one. Let A(bD)
be the algebra of all continuous functions on bD which extend holomorphically
through D. We show that a continuous function f on bD belongs to A(bD) if for
each g in A(bD) the harmonic extension of Re(fg) to D has a single valued
conjugate.
