The case of equality in Landau's problem

Abstract

Kolmogorov (1949) determined the best possible constant Kn,m for the inequality Mm(f)≤Kn,mM0(n−m)/n(f)Mnm/n(f),  0<m<n, where f is any function with n bounded, piecewise continuous derivative on ℝ and Mk(f)=supx∈ℝ|f(k)(x)|. In this paper, we provide a relatively simple proof for the case of equality.