On a class of Hilbert-type inequalities in the whole plane related to exponent function

By introducing a kernel involving an exponent function with multiple parameters, we establish a new Hilbert-type inequality and its equivalent Hardy form. We also prove that the constant factors of the obtained inequalities are the best possible. Furthermore, by introducing the Bernoulli number, Eul...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 13
Main Author You, Minghui
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.02.2021
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Bernoulli number
Euler number
Exponent function
Hilbert-type inequality
Inequalities
Mathematics
Mathematics and Statistics
Partial fraction expansion
47B38
26D10
Exponent function
Euler number
Hilbert-type inequality
Bernoulli number
26D15
Partial fraction expansion
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Summary:By introducing a kernel involving an exponent function with multiple parameters, we establish a new Hilbert-type inequality and its equivalent Hardy form. We also prove that the constant factors of the obtained inequalities are the best possible. Furthermore, by introducing the Bernoulli number, Euler number, and the partial fraction expansion of cotangent function and cosecant function, we get some special and interesting cases of the newly obtained inequality.
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/s13660-021-02563-5