Hilbert-type inequalities with a product-type homogeneous kernel and Schur polynomials
type: Item
instance of: scholarly article
title: Hilbert-type inequalities with a product-type homogeneous kernel and Schur polynomials
zbMATH Open document ID: 1182.26037
author: I. Perić
author: Predrag Vuković
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-08-20T00:00:00Z
review text: The authors generalize some results by \textit{Z. Xie} and \textit{Z. Zheng} [J. Math. Anal. Appl. 339, No. 1, 324--331 (2008; Zbl 1130.26021)] concerning Hilbert-type inequalities for conjugate parameters and with the kernel \[ k(x,y)= (x + a^2y)^{-1}\cdot (x+b^2y)^{-1}\cdot (x+c^2y)^{-1}, \] where \(a>0\), \(b>0\), \(c>0.\) The generalization bases on Hilbert-type inequalities with a kernel that satisfies conditions which ensure that the obtained constants are the best possible ones.
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 5597555
zbMATH Keywords: Hilbert-type inequality
zbMATH Keywords: homogeneous kernel
zbMATH Keywords: best possible constant
zbMATH Keywords: Shur polynomials
zbMATH Keywords: conjugate exponents
reviewed by: Maria Alessandra Ragusa
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.06.046
OpenAlex ID: W2036351248
cites work: Q4146776
cites work: Q5694814
cites work: Q4039929
cites work: Q3283895
cites work: A Hilbert-type integral inequality whose kernel is a homogeneous form of degree \(-3\)
DOI: 10.1016/J.JMAA.2009.06.046
description: scientific article; zbMATH DE number 5597555