Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
Volume 168 / 2005
Studia Mathematica 168 (2005), 25-50
MSC: Primary 45N05, 35K90; Secondary 45K05, 45D05, 46N20.
DOI: 10.4064/sm168-1-3
Abstract
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
