Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation
Abstract
We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2π-periodic functions x with bounded variation of the derivative x′, namely ‖x′‖q⩽K(q,p)‖x‖ap(2πV0(x′))1−alpha, where q ∈ (0, ∞), p ∈ [1, ∞], and α = min{1/2, p/q(p + 1)}.
Published
25.05.2002
How to Cite
Babenko, V. F., V. A. Kofanov, and S. A. Pichugov. “Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 5, May 2002, pp. 603-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4098.
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Section
Research articles