Exact Kolmogorov-Type Inequalities with Bounded Leading Derivative in the Case of Low Smoothness

• Datum: 2001
• Hauptverfasser: Babenko, V. F., Kofanov, V. A., Pichugov, S. A., Бабенко, В. Ф., Кофанов, В. А., Пичугов, С. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2001
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4349
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p ∈ [1, ∞], the following unimprovable inequality holds for functions \(x \in L_\infty ^r \) : $$\left\| {x^{\left( k...