Compact composition operators on model spaces

Let φ: Bd, d≥ 1, be a holomorphic function, where Bd denotes the open unit ball of Cᵈ and D= B₁. Let Θ: D → D be an inner function and let Kᵖ_Θ denote the corresponding model space. For $p>1$, we characterize the compact composition operators C_φ: Kᵖ_Θ → Hᵖ(Bd), where Hᵖ(Bd) denotes the Hardy space.