Sharp Kolmogorov–Remez type inequalities for periodic funtions of a small smoothness

• Datum: 2020
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2020
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/963
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 In the case of either $r = 2, k = 1$ or $r = 3, k = 1, 2,$ for any $q, p \geq 1,$ $\beta \in [0, 2\pi),$ and arbitrary measurable set $B \subset I_{2\pi} := [-\pi/2, 3\pi/2],$ $\mu B \le \beta,$ we prove the sharp Kolmogorov–Remez type inequality$$\|f^{(k)}\|_{q}\leq\frac{\|\varphi_{r-k}\|...