Admissible Banach function spaces and nonuniform stabilities
  For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We generalize a classical theorem of Datko on these spaces. In addition, we obtain new criteria for the existence of nonuniform stability. 
Nicolae Lupa and Liviu Horia Popescu
math.DS math.CA