Sharp Remez type inequalities of various metrics with non-symmetric restrictions on functions

• Date: 2020
• Main Authors: Kofanov, V. A., Popovich, I. V., Кофанов, В. А., Попович, И. В
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2352
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For any $p\in (0, \infty],$ $\omega > 0,$ $\beta \in (0, 2 \omega)$, and arbitrary measurable set $B \subset I_d := [0, d],$ $\mu B \le \beta,$ we obtain the sharp inequality of Remez type$$\|x_{\pm}\|_\infty \le\frac{\|(\varphi+c)_{\pm}\|_\infty}{\|\varphi+c\|_{L_p(I_{2\omega}\...