A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

Krnić, Mario; Pečarić, Josip; Vuković, Predrag

doi:10.1007/s00009-013-0265-1

Cited by 10 publications

(4 citation statements)

References 10 publications

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“…With regard to some other half-discrete inequalities with homogeneous and nonhomogeneous kernels, we refer to [23,[25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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

You

2023

J Inequal Appl

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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.

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“…With regard to some other half-discrete inequalities with homogeneous and nonhomogeneous kernels, we refer to [23,[25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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

You

2023

J Inequal Appl

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“…With regard to other extensions and analogies of (1.2)–(1.4), we can refer to [1,2,8,10,12,14,23–25,27,29,31,36]. In addition, by the continuous innovation of kernel function, introducing parameters, studying the high-dimensional extension, coefficient refinement and the equivalent conditions of the best constant factor, and also considering the discrete and the half-discrete forms, a large number of new Hilbert-type inequalities have been established in recent years (see [4–6,9,11,15,19,20,30,32,34,35,38,39]). It should be pointed that the establishment of these new inequalities fully demonstrates the methods and techniques of analysis and proves to be of vital importance to the development of modern analysis.…”

Section: Introductionmentioning

confidence: 99%

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

You¹

2022

Proceedings of the Edinburgh Mathematical Society

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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.

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“…where the constant factor π is the best possible. With regard to the related results of halfdiscrete Hilbert inequality, we can refer to [33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

On a half-discrete Hilbert-type inequality related to hyperbolic functions

You

2021

J Inequal Appl

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By the introduction of a new half-discrete kernel which is composed of several exponent functions, and using the method of weight coefficient, a Hilbert-type inequality and its equivalent forms involving multiple parameters are established. In addition, it is proved that the constant factors of the newly obtained inequalities are the best possible. Furthermore, by the use of the rational fraction expansion of the tangent function and introducing the Bernoulli numbers, some interesting and special half-discrete Hilbert-type inequalities are presented at the end of the paper.

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A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

Cited by 10 publications

References 10 publications

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

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

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

On a half-discrete Hilbert-type inequality related to hyperbolic functions

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