In this paper we investigate conditions for maximal regularity of Volterra equations defined on the Lebesgue space of sequences $ \ell_p(\mathbb{Z}) $ by using Blünck's theorem on the equivalence between operator-valued $ \ell_p $-multipliers and the notion of $ R $-boundedness. We show sufficient conditions for maximal $ \ell_p-\ell_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.