Maximal L(P)-Regularity For Discrete Time Volterra Equations With Delay

In this paper, we investigate the existence and uniqueness of solutions belonging to the vector-valued space (Formula presented.) by using Blunck’s theorem on the equivalence between operator-valued (Formula presented.) -multipliers and the notion of R-boundedness for the discrete time Volterra equation with delay given by (Formula presented.) where A is a closed linear operator with domain (Formula presented.) defined on a Banach space X, and (Formula presented.) verifies suitable conditions such as 1-regularity. We characterize maximal (Formula presented.) -regularity of solutions of such problems in terms of the data and an spectral condition, and we provide optimal estimates. Moreover, we illustrate our results providing different models that label into our general scheme such as the discrete time wave and Kuznetsov equations.