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 $$\mathcal {S}^p=\{ f\in H(\mathbb D):f'\in H^p(\mathbb D) \}$$ was given for $$1 \le p < \infty $$ by Novinger and Oberlin in 1985. Here, we characterize surjective, not necessarily linear, isometries on $$\mathcal {S}^\infty $$ .