A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function

Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the reverses, and the operator expressions are also given. In particular, the Hardytype inequalities and Hardy-type operators are studied. Additionally, a number of examples with two kinds of particular kernels are considered.

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“…(a) It is evident that (18) and (28) are equivalent for h(t) = k λ (1,t). The same holds for (19) and (29).…”

Section: Yang-hilbert-type Integral Inequalities In the First Quadransupporting

confidence: 53%

Parameterized Yang–Hilbert-Type Integral Inequalities and Their Operator Expressions

Yang

Rassias

2015

Computation, Cryptography, and Network Security

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“…In 2017, Hong [8] also gave two equivalent statements between Hilbert-type inequalities with the general homogenous kernel and parameters. Some other kinds of Hilbert-type inequalities were obtained by [9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane

Xin

Yang

Wang

2018

Journal of Function Spaces

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“…We observe that (16) keeps the form of equality if and only if there exist constants A and B such that they are not all zero and Au λ-λ 2 = Bu λ 1 a.e. in R + .…”

Section: Resultsmentioning

confidence: 96%

On a new extended half-discrete Hilbert’s inequality involving partial sums

2020

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By applying the weight functions, the idea of introducing parameters, and Euler-Maclaurin summation formula, a new extended half-discrete Hilbert's inequality with the homogeneous kernel and the beta, gamma function is given. The equivalent statements of the best possible constant factor related to a few parameters are considered. As applications, a corollary about the case of the non-homogeneous kernel and some particular cases are obtained. MSC: 26D15

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A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function

Cited by 62 publications

References 7 publications

Parameterized Yang–Hilbert-Type Integral Inequalities and Their Operator Expressions

Parameterized Yang–Hilbert-Type Integral Inequalities and Their Operator Expressions

Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane

On a new extended half-discrete Hilbert’s inequality involving partial sums

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