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

You, Minghui

doi:10.1017/s0013091522000360

Cited by 2 publications

(1 citation statement)

References 32 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]).…”

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

Cited by 2 publications

References 32 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 Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

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