Maximal regularity of second order delay equations in Banach spaces

Using known C .-multiplier result, we give necessary and sufficient conditions for the second order delay equations: u..(t)=Au(t)+Fut+Gu.t+f(t),t.R to have maximal regularity in Hölder continuous function spaces C .(., X), where X is a Banach space, A is a closed operator in X, F, G . .(C([.r, 0],X), X) are delay operators for some fixed r > 0.