Fourier Multipliers and Integro‐Differential Equations in Banach Spaces

Abstract

Operator-valued Fourier multiplier theorems are used to establish maximal regularity results for an integro-differential equation with infinite delay in Banach spaces. Results are obtained under general conditions for periodic solutions in the vector-valued Lebesgue and Besov spaces. The latter scale includes in particular the Hölder spaces Cα, 0 < α < 1.