Periodic solutions of delay equations in Besov spaces and Triebel-Lizorkin spaces. (English) Zbl 1179.34085
Summary: Under suitable assumptions on the Fourier transform of the delay operator \(F\), we give necessary and sufficient conditions for the inhomogeneous abstract delay equations: \(u'(t) = Au(t) + Fu_t + f(t)\), \((t\in\mathbb T)\) to have maximal regularity in Besov spaces \(B^s_{p,q}(\mathbb T, X)\) and Triebel-Lizorkin spaces \(^s_{p,q}(\mathbb T, X)\).
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 34C25 | Periodic solutions to ordinary differential equations |
