Compact composition operators on model spaces

Doubtsov, Evgueni 

Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1109-1115

Résumé

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

Détail

DOI : 10.4153/S0008439524000675

Mots-clés : Model spaces, composition operator, Nevanlinna counting function, real interpolation of Banach spaces