A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function

In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hi...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2023; no. 1; pp. 43 - 15
Main Author You, Minghui
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 24.03.2023
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Half-discrete
Hardy-type inequality
Hilbert-type inequality
Homogeneous kernel
Inequalities
Inequality
Kernel functions
Mathematics
Mathematics and Statistics
Nonhomogeneous kernel
Parameters
Weighting functions
47B38
26D10
Nonhomogeneous kernel
Hardy-type inequality
Hilbert-type inequality
Half-discrete
Homogeneous kernel
26D15
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Summary:In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Finally, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-02951-z