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

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...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 65; no. 3; pp. 833 - 846
Main Author You, Minghui
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2022
Subjects
Inequalities
Inequality
Kernel functions
Mathematical functions
Weighting functions
47B38
weight function
classical kernel functions
26D10
partial fraction expansion
Hilbert-type inequality
whole plane
26D15
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091522000360