The Hardy inequalities
type: Item
instance of: scholarly article
title: The Hardy inequalities
zbMATH Open document ID: 0801.26007
DOI: 10.1007/BF01210443
published in: Mathematical Notes
publication date: 1994-04-12T00:00:00Z
review text: Using the Fourier transform, the author proves that \[ \| f^{(k)} \| \leq {n - k \over k} h^{ - k} \cdot 2^{ - m} \bigl \| \Delta^ m_{\pi h} (f) \bigr \| + {k \over n} h^{n - k} \| f^{(n)} \| \] for any \(f \in L_ 2 (\mathbb{R})\) with an absolutely continuous derivative \(f^{(n - 1)}\). Here \(0 < m < k < n\) are given integers, \(\| \cdot \|\) is the norm in \(L_ 2 (\mathbb{R})\) and the symbol \(\Delta^ m_{\pi h}\) \((h > 0)\) stands for the difference operator of the order \(m\) with the step \(\pi h\).
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 525738
zbMATH Keywords: Hardy inequality
zbMATH Keywords: Plancherel theorem
zbMATH Keywords: Fourier transform
zbMATH Keywords: difference operator
author: L. V. Taĭkov
reviewed by: Bohumír Opic
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 525738