The case of equality in Landau's problem
type: Item
instance of: scholarly article
title: The case of equality in Landau's problem
zbMATH Open document ID: 1077.26008
DOI: 10.1155/IJMMS.2005.1781
author: Yanyan Li
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-12-07T00:00:00Z
full work available at URL: https://eudml.org/doc/51867
review text: Summary: Kolmogorov (1949) determined the best possible constant \(K_{n, m}\) for the inequality \[ M_m (f) \leq K_{n, m}M^{(n-m)/n}_0 (f) M_n^{m/n}(f), \quad 0 < m < n, \] where \(f\) is any function with \(n\) bounded, piecewise continuous derivatives on \(\mathbb{R}\) and \(M_k(f) = \sup_{x \in \mathbb{R}}|f^{(k)}(x)|\). In this paper, we provide a relatively simple proof for the case of equality.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 2236285
zbMATH Keywords: Landau inequality
zbMATH Keywords: derivatives
MaRDI profile type: Publication
description: scientific article