Exact constant in the Dzyadyk inequality for the derivative of an algebraic polynomial

• Date: 2017
• Main Authors: Galan, V. D., Shevchuk, I. A., Галан, В. Д., Шевчук, І. О.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1721
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For natural $k$ and $n \geq 2k$, we determine the exact constant $c(n, k)$ in the Dzyadyk inequality $$|| P^{\prime}_n\varphi^{1-k}_n ||_{C[ 1,1]} \leq c(n, k)n\| P_n\varphi^{-k}_n \|_{C[ 1,1]}$$ for the derivative $P^{\prime}_n$ of an algebraic polynomial $P_n$ of degree $\leq n$, where $$\varph...