On inequalities for the norms of intermediate derivatives of multiply monotone functions defined on a finite segment

• Date: 2012
• Main Authors: Skorokhodov, D. S., Скороходов, Д. С.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2592
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the following modification of the Landau-Kolmogorov problem: Let $k, r \in \mathbb{N}, \quad 1 \leq k \leq r -1$ and $p, q, s \in [1, \infty]$. Also let $MM^m,\; m \in \mathbb{N}$, be the class of nonnegative functions defined on the segment $[0,1]$ whose derivatives of orders $1, 2,......