Discrete maximal regularity for Volterra equations and nonlocal time-stepping schemes

[EN] In this paper we investigate conditions for maximal regularity of Volterra equations defined on the Lebesgue space of sequences l(p)(Z) by using Blunck's theorem on the equivalence between operator-valued l(p)-multipliers and the notion of R-boundedness. We show sufficient conditions for maximal l(p) - l(q) regularity of solutions of such problems solely in terms of the data. We also explain the significance of kernel sequences in the theory of viscoelasticity, establishing a new and surprising connection with schemes of approximation of fractional models.