Surjective isometries on function spaces with derivatives

Abstract: Let $A$ be a complex Banach space with a norm $|f|=|f|_X+|d(f)|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $|\cdot|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,|\cdot|)$, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.