A note on Weyl type discrete inequalities
type: Item
instance of: scholarly article
title: A note on Weyl type discrete inequalities
zbMATH Open document ID: 0869.26005
author: B. G. Pachpatte
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-17T00:00:00Z
review text: The author used elementary methods to prove that for \(\alpha\geq0\), \(p\geq0\), \(q\geq1\) and for a sequence of real numbers \(\{u_n\}_{n=0}^m\) the inequality \[ \sum_{n=0}^{m-1}|u_n|^{p+q} \leq M \Bigl\{\sum_{n=0}^{m-1}a_n|u_n|^p \bigl(|u_n|m^{-1} + |u_{n+1}-u_n|\bigr)^q\Bigr\}^{1/q} \Bigl\{\sum_{n=0}^{m-1}b_n|u_n|^{p+q}\Bigr\}^{1/q'} \] holds with a constant \(M\) depending on \(\alpha\), \(p\), \(q\), and with certain coefficients \(a_n\), \(b_n\) depending on \(\alpha\) and \(q\). Letting \(m\to\infty\) for a particular choice of parameters and coefficients he obtained a discrete analogue of the Weyl inequality as a consequence.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 710350
zbMATH Keywords: discrete inequality
zbMATH Keywords: Weyl inequality
reviewed by: Jiří Rákosník
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1455
OpenAlex ID: W2095259127
DOI: 10.1006/JMAA.1994.1455
description: scientific article; zbMATH DE number 710350