Compact composition operators on model spaces

Let $φ: B_d\to\mathbb{D}$, $d\ge 1$, be a holomorphic function, where $B_d$ denotes the open unit ball of $\mathbb{C}^d$ and $\mathbb{D}= B_1$. Let $Θ: \mathbb{D} \to \mathbb{D}$ be an inner function and let $K^p_Θ$ denote the corresponding model space. For $p>1$, we characterize the compact composition operators $C_φ: K^p_Θ\to H^p(B_d)$, where $H^p(B_d)$ denotes the Hardy space.

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