Maximal regularity for perturbed integral equations on the line
The authors characterize the existence and uniqueness of solutions for a perturbed linear integral equation with infinite delay in Hölder spaces. The method is based on the theory of operator-valued Fourier multipliers. This paper is well written and it is nice to read. We note that the most important tools to prove maximal regularity are Fourier multiplier theorems. They play a key role in the analysis of elliptic and parabolic problems. In particular, the theory of operator-valued Fourier multiplier is applied to obtain results on the hyperbolicity of delay equations, to obtain stability of linear control systems in Banach spaces, to study maximal regularity for difference equations. Some complementary references to this paper are the following: \textit{A. Bátkai, E. Fašanga} and \textit{R. Shvidkoy} [Acta Sci. Math. 69, No. 1--2, 131--145 (2003; Zbl 1050.35120)]; \textit{C. Cuevas} and \textit{C. Vidal} [Adv. Difference Equ. 2006, Article ID 97614, 11 p. (2006; Zbl 1133.39001)]; \textit{A. Castro} and \textit{C. Cuevas} [J. Difference Equ. Appl. 17, No. 3, 327--358 (2011; Zbl 1220.39005)]; \textit{Y. Latushkin} and \textit{F. Räbiger} [Integral Equations Oper. Theory 51, No. 3, 375--394 (2005; Zbl 1077.47042)].
scientific article; zbMATH DE number 6153948
scientific article