On Inequalities of the Landau–Kolmogorov–Hörmander Type on a Segment and Real Straight Line

Abstract

We prove inequalities of the Landau–Kolmogorov–Hörmander type for the uniform norms (on some subinterval) of positive and negative parts of intermediate derivatives of functions defined on a finite interval. By using the limit transition, we obtain a new proof or the well-known Hörmander result.