Sharp Remez type inequalities estimating the $L_q$ -norm of a function via its $L_p$ -norm

• Date: 2022
• Main Authors: Kofanov, V. A., Olexandrova, T. V., Кофанов, Владимир Александрович, Кофанов, В. О., Олександрова, Т. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6836
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For any $q\geq p>0,$ $\alpha=(r+1/q)/(r+1/p),$ $f_p\in[0,\infty],$ $\beta\in[0,2\pi),$ we prove the sharp Remez type inequality $$\|x\|_q\leq\frac{\|\varphi_r+c\|_q}{\|\varphi_r+ c\|^{\alpha}_{L_p([0,2\pi]\setminus B_{y(\beta)})}}\|x\|^{\alpha}_{L_p([0,2\pi]\setminus B)}\|x^{(r)...