A Hilbert-type inequality in the whole plane with the constant factor related to some special constants

You, Minghui; Dong, Fang; He, Zhen ua

doi:10.7153/jmi-2022-16-03

Cited by 3 publications

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“…Such inequalities as (1.3) and (1.4) are commonly known as Hilbert-type inequalities. It should be pointed out that, by introducing new kernel functions, and considering the coefficient refinement, reverse form, multidimensional extension, a large number of Hilbert-type inequalities were established in the past 20 years (see [12][13][14][15][16][17][18][19][20][21][22][23]).…”

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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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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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Construction of a class of half-discrete Hilbert-type inequalities in the whole plane

You

2024

Open Mathematics

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In this work, we first define two special sets of real numbers, and then, we construct a half-discrete kernel function where the variables are defined in the whole plane, and the parameters in the kernel function are limited to the newly constructed special sets. Estimate the kernel function in the whole plane by converting it to the first quadrant, and then, a class of new Hilbert-type inequality is established. Additionally, it is proved that the constant factor of the newly established inequality is the best possible. Furthermore, assigning special values to the parameters and using rational fraction expansion of cosecant function, some special results are presented at the end of this article.

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On a Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

Yang,

2024

Mathematics

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In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to the parameters and deal with the equivalent inequalities. Our main result provided a new generalization of Hardy–Littlewood–Polya inequality, and as a consequence, we show that some new inequalities of the Hardy–Littlewood–Polya type can be derived from the current results by taking the special values of parameters.

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A Hilbert-type inequality in the whole plane with the constant factor related to some special constants

Cited by 3 publications

References 0 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

Construction of a class of half-discrete Hilbert-type inequalities in the whole plane

On a Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

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