Hilbert-type inequalities with a product-type homogeneous kernel and Schur polynomials

The main objective of this paper is to prove Hilbert-type and Hardy–Hilbert-type inequalities with a product-type homogeneous kernel, thus generalizing a result obtained in [Z. Xie, Z. Zheng, A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3, J. Math. Anal. Appl. 339...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-11, Vol.359 (2), p.786-793
Main Authors: PERIC, Ivan, VUKOVIC, Predrag
Format: Article
Language:English
Subjects:
Conjugate exponents
Divided differences
Exact sciences and technology
Hilbert-type inequality
Homogeneous kernel
Mathematical analysis
Mathematics
Schur polynomials
Sciences and techniques of general use
The best possible constant
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Summary:The main objective of this paper is to prove Hilbert-type and Hardy–Hilbert-type inequalities with a product-type homogeneous kernel, thus generalizing a result obtained in [Z. Xie, Z. Zheng, A Hilbert-type integral inequality whose kernel is a homogeneous form of degree −3, J. Math. Anal. Appl. 339 (2008) 324–331]. In some cases the best possible constants obtained in these inequalities are expressed using the Schur polynomials.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.06.046