On sharp Kolmogorov-type inequalities taking into account the number of sign changes of derivatives

• Date: 2008
• Main Authors: Kofanov, V. A., Miropol'skii, V. E., Кофанов, В. А., Миропольский, В. Е.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3278
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

New sharp inequalities of the Kolmogorov type are established, in particular, the following sharp inequality for $2 \pi$-periodic functions $x \in L^r_{\infty}(T):$ $$||x^{(k)}||_l \leq \left(\frac{\nu(x')}{2} \right)^{\left(1 - \frac1p \right)\alpha} \frac{||\varphi_{r-k}||_l}{||\varphi_r...