Sharp Remez-type inequalities of various metrics in the classes of functions with а given comparison function

• Date: 2017
• Main Authors: Gaydabura, A. E., Kofanov, V. A., Гайдабура, А. Е., Кофанов, В. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1796
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For any $p \in [1,\infty ],\; \omega > 0, \;\beta \in (0, 2\omega )$, and any measurable set $B \subset I_d := [0, d], \mu B \leq \beta$, we obtain the following sharp Remez-type inequality of various metrics $$E_0(x)\infty \leq \frac{\| \varphi \|_{\infty} }{E_0 (\varphi )L_p(I_{2\ome...