H(b) spaces of non-extreme b over finitely connected planar domains

Abstract In this work, density of the algebra A ( D ) $\mathcal{A}\left(D\right)$ in H(b) spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra is considered when the defining function b is a non-extreme point of the unit ball of H ∞(D). In the last part boundedness of composition operators on H(b) spaces is considered and as well as a generalization of the unit disk case is given, the boundedness of composition operators with generalized Blaschke symbols over finitely connected domains is characterized.