New kinds of Hardy-Hilbert's integral inequalities
type: Item
instance of: scholarly article
title: New kinds of Hardy-Hilbert's integral inequalities
zbMATH Open document ID: 1231.26021
author: W. T. Sulaiman
published in: Applied Mathematics Letters
publication date: 2010-04-14T00:00:00Z
review text: The paper establishes a generalized weighted Hardy-Hilbert's integral inequality, \[ \begin{multlined} \int_0^{\infty} \int_0^{\infty} \frac {f(x)g(x)}{h(x,y)\max\left\{k\left(\frac xy\right),k\left(\frac yx\right)\right\}} dxdy\\ \leq C \left(\int_0^{\infty} t^{1-\lambda}f^p(t)dt \right)^{1/p} \left( \int_0^{\infty} t^{1-\lambda} g^q(t)dt \right)^{1/q}, \end{multlined} \] where \(h\) is homogeneous of degree \(\lambda\) and \(k\) is non-decreasing. A value of the constant \(C\) is given as the sum of two integrals involving \(h\) and \(k\). The technique of the proof is basically Holder's inequality and estimation of integrals. The inequality is applied to some specifically selected functions of \(h\) and \(k\), and the corresponding inequalities involving Beta and Gamma functions are obtained.
reviewed by: Tieling Chen
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 5692714
MaRDI profile type: Publication
full work available at URL: j.aml.2009.10.011
OpenAlex ID: W2074414182
cites work: Q5812325
cites work: Q4000235
cites work: Q5433762
cites work: A new Hilbert-type integral inequality and the equivalent form
DOI: 10.1016/J.AML.2009.10.011
description: scientific article; zbMATH DE number 5692714