Landau-type inequalities and \(L^p\)-bounded solutions of neutral delay systems (Q1970043)

In this paper various forms of Landau inequalities \(\|y^{(m)}\|^n\leq \lambda\|y\|^{n-m}\|y^{(n)}\|^m\) and Halperin--Pitt inequalities \(\|y^{(m)}\|\leq \varepsilon\|y^{(n)}\|+S(\varepsilon)\|y\|\) are discussed for arbitrary norms, intervals and vector-valued functions \(y\). Concrete function spaces are then involved, namely Lebesgue, Orlicz and Stepanov spaces. The results are applied to obtaining Esclagon--Landau theorems for solutions of linear neutral delay difference--differential systems.