Abstract
In Section 1 relations between various forms of Landau inequalities ‖y(m)‖n≤λ‖y‖n−m‖y(n)‖m and Halperin–Pitt inequalities ‖y(m)‖≤ε‖y(n)‖+S(ε)‖y‖ are discussed, for arbitrary norms, intervals and Banach-space-valued y. In Section 2 such inequalities are derived for weighted LP-norms, Stepanoff- and Orlicz-norms.
With this, Esclangon–Landau theorems for solutions y of linear neutral delay difference-
differential systems are obtained: If y is bounded e.g. in a weighted LP- or Stepanoff-norm, then so are the y(m). This holds also for some nonlinear functional differential equations.