Discrete Maximal Regularity for Volterra Equations and Nonlocal Time-Stepping Schemes

In this paper we investigate conditions for maximal regularity of Volterra equations defined on the Lebesgue space of sequences `p(Z) by using Blünck’s theorem on the equivalence between operator-valued `p-multipliers and the notion of R-boundedness. We show sufficient conditions for maximal `p − `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. © 2020 American Institute of Mathematical Sciences. All rights reserved.