On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives

• Datum: 2003
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2003
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3919
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

For 2π-periodic functions \(x \in L_\infty ^r \) and arbitrary q ∈ [1, ∞] and p ∈ (0, ∞], we obtain the new exact Kolmogorov-type inequality \(|| x^(k) ||_q \leqslant (\frac{v(x^(k))}{2})^{1/q} \frac{|| \phi_{r-k} ||_q}{||| \phi_r |||_p^\alpha} ||| x |||_p^\alpha || x^(r) ||_\infty^{1- \alpha}...