Surjective isometries on a Banach space of analytic functions with bounded derivatives

Abstract

Let $H(\mathbb{D})$ be the linear space of all analytic functions on the open unit disc $\mathbb{D}$ and $H^p(\mathbb{D})$ the Hardy space on $\mathbb{D}$. The characterization of complex linear isometries on ${\mathcal{S}}^p=\{f\in H(\mathbb{D}):f^{\prime }\in H^p(\mathbb{D})\}$ was given for $1\le p<\infty$ by Novinger and Oberlin in 1985. Here, we characterize surjective, not necessarily linear, isometries on ${\mathcal{S}}^{\infty }$.