An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators

The aim of this paper is to study the connection between the (non)uniform exponential dichotomy of a non(uniform) exponentially bounded, strongly continuous evolution family and the admissibility of some function spaces. Thus, there are extended recent results established by L. Barreira and C. Valls (2010, 2011) in [10] and [11].