Reducibility and unitary equivalence of analytic multipliers on Sobolev disk algebra

It is proved that Mϕ with 2-Blaschke product ϕ is reducible on Sobolev disk algebra R(D) if and only if ϕ=βα−z21−α‾z2 for some α∈D and unimodular constant β. Also, an analytic multiplier Mϕ is unitary equivalent to Mzn on R(D) if and only if ϕ=λzn for some unimodular constant λ.