Reducibility and unitary equivalence of analytic multipliers on Sobolev disk algebra

It is proved that M ϕ with 2-Blaschke product ϕ is reducible on Sobolev disk algebra R ( D ) if and only if ϕ = β α − z 2 1 − α ‾ z 2 for some α ∈ D and unimodular constant β . Also, an analytic multiplier M ϕ is unitary equivalent to M z n on R ( D ) if and only if ϕ = λ z n for some unimodular constant λ .