New extensions of Hilbert’s inequality with multiple parameters

Chen, Z. Q.; Xu, Jinde

doi:10.1007/s10474-007-6135-1

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…Hardy [4], Mulholland [14], [15], Bonsall [1] and Levin [12]. Discrete Hilbert inequalities with non-homogeneous kernels were studied in [2], [3], [7], [8]- [11], [16], [17], [19]- [24].…”

Section: Fundamental Contributions Have Been Given To This Classical mentioning

confidence: 99%

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Discrete Hilbert type inequality with non-homogeneous kernel

Draščić

Pogány

2009

APPL ANAL DISCRETE M

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“…Hardy [4], Mulholland [14], [15], Bonsall [1] and Levin [12]. Discrete Hilbert inequalities with non-homogeneous kernels were studied in [2], [3], [7], [8]- [11], [16], [17], [19]- [24].…”

Section: Fundamental Contributions Have Been Given To This Classical mentioning

confidence: 99%

“…where a, b are nonnegative; K(•, •) we call kernel function of the double series (2). So, to obtain discrete Hilbert type inequalities (or in other words -double series theorems) one derives sharp upper bounds for H a,b K in terms of weighted p -norms of a, b.…”

Section: Fundamental Contributions Have Been Given To This Classical mentioning

confidence: 99%

Discrete Hilbert type inequality with non-homogeneous kernel

Draščić

Pogány

2009

APPL ANAL DISCRETE M

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“…Recent interest in this area is shown by Gao, Debnath, Pachpatte, Yang, Krnić and Pečarić, among others. The reference list of this paper contains mainly publications with discrete Hilbert's inequalities with non-homegeneous kernels [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], since this version of a Hilbert's-type inequality is in the focus of our interest. The usual way to obtain a Hilbert's inequality is to apply the Hölder inequality to a conveniently rewritten bilinear form…”

Section: Introductionmentioning

confidence: 99%

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

Pogány

2022

Axioms

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The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively investigated non-homogeneous kernel, which mutually covers the homogeneous kernel cases as well. Particularly, novel Hilbert’s double series inequality results are presented, which include the upper bounds built exclusively with non-weighted ℓp–norms. The main mathematical tools are the integral expression of Mathieu (a, λ)-series, the Hölder inequality and a generalization of the double series theorem by Yang.

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“…Regarding extensions of (1.4), we can refer to [12][13][14][15][16]. In addition, some extensions of (1.2) were also established in the past 20 years (see [10,11,[17][18][19][20]).…”

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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New extensions of Hilbert’s inequality with multiple parameters

Cited by 7 publications

References 10 publications

Discrete Hilbert type inequality with non-homogeneous kernel

Discrete Hilbert type inequality with non-homogeneous kernel

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

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

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