Exponential functions as boundary layer functions.
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.