On Inequalities of the Landau–Kolmogorov–Hörmander Type on a Segment and Real Straight Line - Kofanov, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
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.