International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1781-1793
doi:10.1155/IJMMS.2005.1781
The case of equality in Landau's problem
G.W. Hagerty1
and P. Nag2
1Department of Mathematics, Black Hills State University, Spearfish 57799-9115, SD, USA
2Department of Mathematics, Black Hills State University, Spearfish 57799-9127, SD, USA
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.