On a new generalization of some Hilbert-type inequalities

In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also c...

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Published inOpen mathematics (Warsaw, Poland) Vol. 19; no. 1; pp. 569 - 582
Main Authors You, Minghui, Song, Wei, Wang, Xiaoyu
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 09.07.2021
De Gruyter Poland
Subjects
26D15
41A17
Bernoulli number
Euler number
Hilbert-type inequality
Inequalities
Kernel functions
partial fraction expansion
Trigonometric functions
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Abstract In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.
AbstractList In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.
Author You, Minghui
Song, Wei
Wang, Xiaoyu
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  surname: Wang
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SubjectTerms 26D15
41A17
Bernoulli number
Euler number
Hilbert-type inequality
Inequalities
Kernel functions
partial fraction expansion
Trigonometric functions
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Title On a new generalization of some Hilbert-type inequalities
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