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On a class of Hilbert-type inequalities in the whole plane involving some classical kernel functions

Part of: Special classes of linear operators Inequalities

Published online by Cambridge University Press:  06 October 2022

Minghui You Open the ORCID record for Minghui You [Opens in a new window]
Minghui You*
Affiliation:
Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China (youminghui@zime.edu.cn)
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Abstract

In this paper, by the introduction of several parameters, we construct a new kernel function which is defined in the whole plane and includes some classical kernel functions. Estimating the weight functions with the techniques of real analysis, we establish a new Hilbert-type inequality in the whole plane, and the constant factor of the newly obtained inequality is proved to be the best possible. Additionally, by means of the partial fraction expansion of the tangent function, some special and interesting inequalities are presented at the end of the paper.

Keywords

Hilbert-type inequalityweight functionpartial fraction expansionwhole planeclassical kernel functions

MSC classification

Primary: 26D15: Inequalities for sums, series and integrals 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 47B38: Operators on function spaces (general)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 3 , August 2022 , pp. 833 - 846
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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