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

  • * Corresponding author: Carlos Lizama

    * Corresponding author: Carlos Lizama 

The first author is supported by FONDECYT grant 1180041

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  • 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.

    Mathematics Subject Classification: Primary: 49M25, 49N60; Secondary: 42A45, 47A58.


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