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

Abstract In this work, density of the algebra A (D) A (D) 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.