Inequalities of Different Metrics for Differentiable Periodic Functions, Polynomials, and Splines

• Date: 2001
• Main Authors: Kofanov, V. A., Кофанов, В. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4283
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain new inequalities of different metrics for differentiable periodic functions. In particular, for p, q ∈ (0, ∞], q > p, and s ∈ [p, q], we prove that functions \(x \in L_\infty ^{{\text{ }}r}\) satisfy the unimprovable inequality $$|| (x-c_{s+1} (x))_{\pm} ||_q \leqslant \frac{|...