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

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