On some new inequalities similar to Hilbert's inequality
type: Item
instance of: scholarly article
title: On some new inequalities similar to Hilbert's inequality
zbMATH Open document ID: 0911.26012
author: B. G. Pachpatte
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-26T00:00:00Z
review text: Let \(p,q\in [1,\infty)\), \(k,r\in\mathbb{N}\), \(\{a_m\}^k_1,\{b_n\}^r_1\subset [0,\infty)\), \(A_m= \sum^m_{s=1} a_s\) and \(B_n= \sum^n_{t=1} b_t\). Then \[ \sum^k_{m= 1} \sum^r_{n= 1} {A^p_m B^q_n\over m+n}\leq C\Biggl(\sum^k_{m= 1} (k- m+1) (A^{p-1}_m a_m)^2\Biggr)^{1/2} \Biggl(\sum^r_{n= 1}(r- n+1) (B^{q- 1}_n b_n)^2\Biggr)^{1/2} \] (unless \(\{a_m\}^k_1\subset \{0\}\) or \(\{b_n\}^r_1\subset \{0\}\)), where \(C= 2^{-1} pq\sqrt{kr}\). This is one of the main results of the paper, the others are its modifications. Note that integral analogues of the mentioned results are also proved.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1216737
zbMATH Keywords: Hilbert-type inequalities
reviewed by: Bohumír Opic
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6043
OpenAlex ID: W2031752698
cites work: ON AN INEQUALITY OF HARDY'S (II)
cites work: On Hilbert's inequality and its applications
cites work: Analytic Inequalities
cites work: On inequalities of Hilbert and Widder
cites work: Q5632833
cites work: Q4881109
DOI: 10.1006/JMAA.1998.6043
description: scientific article; zbMATH DE number 1216737