PERIODIC SOLUTIONS OF DELAY EQUATIONS IN BESOV SPACES AND TRIEBEL-LIZORKIN SPACES

Abstract

Under suitable assumptions on the Fourier transform of the delay operator $F$, we give necessary and sufficient conditions for the inhomogeneous abstract delay equations: $ u'(t)=Au(t)+Fu_{t}+f(t), \ (t\in \mathbf T)$ to have maximal regularity in Besov spaces $B_{p,q}^s(\mathbf T, X)$ and Triebel-Lizorkin spaces $F_{p,q}^s(\mathbf T, X)$. .