On Kolmogorov-Type Inequalities with Integrable Highest Derivative

• Date: 2002
• Main Authors: Babenko, V. F., Kofanov, V. A., Pichugov, S. A., Бабенко, В. Ф., Кофанов, В. А., Пичугов, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4208
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain the new exact Kolmogorov-type inequality $$\left\| {x^{\left( k \right)} } \right\|_2 \leqslant K\left\| x \right\|_2^{\frac{{r - k - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}{{r - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace}...