The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
Bing He,Yong Hong,Qiang Chen +2 more
About: This article is published in Open Mathematics. The article was published on 25 May 2021. and is currently open access. The article focuses on the topics: Multiple integral & Class (set theory).
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Citations
An Extended Hilbert-Type Inequality with Two Internal Variables Involving One Partial Sums
Aizhen Wang,Bicheng Yang +1 more
TL;DR: An extended Hilbert-type inequality with two internal variables involving one partial sums is established. The inequality is a refinement of a published inequality and provides equivalent conditions for the best possible constant.
1
Optimal matching parameters of the inverse Hilbert-type integral inequality with quasihomogeneous kernels and their applications
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TL;DR: Optimal matching parameters of the inverse Hilbert-type integral inequality with quasihomogeneous kernels are established using the inverse Hölder inequality and the weight function method.
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A refined Hardy-Littlewood-Polya inequality and the equivalent forms
Abstract: . In this article, by the Euler-Maclaurin summation formula, we construct proper weight coef fi cients and use them to establish a re fi ned Hardy-Littlewood-Polya inequality with multi parameters. Based on this inequality, the equivalent statements of the best possible constant factor related to several parameters are discussed. The equivalent forms, some particular inequalities and the operator expressions of the obtained inequalities are considered.
A New Reverse Extended Hardy–Hilbert’s Inequality with Two Partial Sums and Parameters
Jian Quan Liao,Bicheng Yang +1 more
TL;DR: In this paper , a reverse extended Hardy-Hilbert's inequality with two partial sums and multi-parameters was obtained by using the methods of real analysis and the mid-value theorem.
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Optimal Matching Parameters for the Inverse Hilbert-Type Integral Inequality with Quasihomogeneous Kernels and Their Applications
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References
On Some Extensions of Hardy-Hilbert's Inequality and Applications
TL;DR: Azar et al. as mentioned in this paper established an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series by introducing some parameters, and they considered reverses, some particular results and their equivalent forms.
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Half-Discrete Hilbert-Type Inequalities
Bicheng Yang,Lokenath Debnath +1 more
- 24 Dec 2013
TL;DR: In this paper, the Euler - Maclaurin's Summation Formula was improved with the general non-homogeneous kernel and extensions of Hilbert-type Inequalities.
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On a multidimensional version of the Hilbert type inequality
Mario Krnić,Predrag Vuković +1 more
TL;DR: In this paper, the main objective of this paper is a study of some new multidimensional Hilbert type inequalities with a general homogeneous kernel, and the conditions under which the constant factors included in the obtained inequalities are the best possible.
48
On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters
TL;DR: In this article, the Hilbert's and Hardy-Hilbert integral inequalities in the non-conjugate case were shown to be the best possible, when the parameters satisfy appropriate conditions.
Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel
TL;DR: In this paper, the validity of the following half-discrete Hilbert-type multiple integral inequality (MIMI) has been studied and its applications in operator theory are discussed.