Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation

• 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/4098
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2π-periodic functions x with bounded variation of the derivative x′, namely $$\left\| {x'} \right\|_q \leqslant K\left( {q,p} \right)\left\| x \right\|_p^a \left( {\mathop V\limits_{0}^{{2\pi }} \left( {x'...