Abstract
We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2π-periodic functions x with bounded variation of the derivative x′, namely
where q ∈ (0, ∞), p ∈ [1, ∞], and α = min{1/2, p/q(p + 1)}.
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Babenko, V.F., Kofanov, V.A. & Pichugov, S.A. Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation. Ukrainian Mathematical Journal 54, 741–749 (2002). https://doi.org/10.1023/A:1021675111923
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DOI: https://doi.org/10.1023/A:1021675111923