Interpolation and duality in spaces of pseudocontinuable functions

Abstract Given an inner function $$\theta $$ θ on the unit disk, let $$K^p_\theta :=H^p\cap \theta {\overline{z}}\overline{H^p}$$ K p : = H ∩ z ¯ be associated star-invariant subspace of Hardy space $$H^p$$ . Also, we put $$K_{*\theta }:=K^2_\theta \cap \mathrm{BMO}$$ ∗ 2 BMO Assuming that $$B=B_{{\mathcal {Z}}}$$ B Z is interpolating Blaschke product with zeros $${\mathcal {Z}}=\{z_j\}$$ { j } , characterize, for a number smoothness classes X sequences values {W}}=\{w_j\}$$ W w such interpolation problem $$f\big |_{{\mathcal {Z}}}={\mathcal {W}}$$ f | has solution f in $$K^2_B\cap X$$ X Turning to case general further establish non-duality relation between $$K^1_\theta 1 and }$$ Namely, prove latter properly contained dual former, unless finite product. From this derive amusing non-interpolation result functions $$K_{*B}$$ as above.