A Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree \(-2\)
type: Item
instance of: scholarly article
title: A Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree \(-2\)
zbMATH Open document ID: 1218.26031
DOI: 10.1155/2011/401428
author: Dongmei Xin
author: Bicheng Yang
published in: Journal of Inequalities and Applications
publication date: 2011-05-13T00:00:00Z
full work available at URL: https://eudml.org/doc/233669
review text: Assume that \(f(x)\) and \(g(x)\) are non-negative and both of them satisfy \(0<\int_0^\infty f^2(x)\,dx<\infty\). Then, Hilbert's integral inequality asserts that \[ \int_0^\infty \int_0^\infty \frac{f(x)g(y)}{x+y}\,dx\,dy< \pi\left(\int_0^\infty f^2(x)\,dx\int_0^\infty g^2(x)\,dx\right)^\frac12, \] where \(\pi\) is the best possible constant. The main object of the paper is to give a new Hilbert-type inequality in the whole plane with a homogeneous kernel of degree \(-2\) involving some parameters and a best constant factor.
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 5887677
zbMATH Keywords: Hilbert's integral inequality
Wikidata QID: Q59267060
MaRDI profile type: Publication
OpenAlex ID: W1975398841
cites work: Q5812325
cites work: Q4000235
cites work: Q5062940
cites work: On the norm of an integral operator and applications
cites work: Q5062755
cites work: On the norm of a Hilbert's type linear operator and applications
cites work: Q5872255
cites work: A new Hilbert-type inequality
cites work: On a new Hilbert-type integral inequality with the integral in whole plane
description: scientific article; zbMATH DE number 5887677