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Kolmogorov (1949) determined the best possible constant K n,m for the inequality M m (f) ≤ K n,m M (n−m)/n 0 (f)M m/n n (f), 0 < m < n, where f is any function with n bounded, piecewise continuous derivative on R and M k (f) = sup x∈R | f (k) (x)|. In this paper, we provide a relatively simple proof for the case of equality.

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