Abstract
We obtain the new exact Kolmogorov-type inequality
for 2π-periodic functions \(x \in L_1^r\) and any k, r ∈ N, k < r. We present applications of this inequality to problems of approximation of one class of functions by another class and estimates of K-functional type.
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Babenko, V.F., Kofanov, V.A. & Pichugov, S.A. On Kolmogorov-Type Inequalities with Integrable Highest Derivative. Ukrainian Mathematical Journal 54, 2055–2059 (2002). https://doi.org/10.1023/A:1024085601336
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DOI: https://doi.org/10.1023/A:1024085601336