scholarly journals On two new multidimensional integral inequalities of the Hilbert type

2000 ◽  
Vol 31 (2) ◽  
pp. 123-130
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequalities ◽  
Hilbert’S Inequality ◽  
Elementary Analysis ◽  
Multidimensional Integral ◽  
Integral Analogue ◽  
Hilbert Type

The main aim of this paper is to establish two new multidimensional integral inequalities similar to the integral analogue of the well known Hilbert's inequality by using elementary analysis.

scholarly journals INEQUALITIES SIMILAR TO THE INTEGRAL ANALOGUE OF HILBERT'S INEQUALITY

1999 ◽  
Vol 30 (2) ◽  
pp. 139-146
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Hilbert’S Inequality ◽  
Elementary Analysis ◽  
Integral Analogue ◽  
New Inequalities

In the present paper we establish some new inequalities similar to the integral ana­logue of Hilbert's inequality by using a fairly elementary analysis.

scholarly journals On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xingshou Huang ◽  
Bicheng Yang
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Real Analysis ◽  
Homogeneous Kernel ◽  
Hilbert’S Inequality ◽  
The Best Possible Constant ◽  
Hilbert Type ◽  
Weight Coefficients

AbstractBy the use of the weight coefficients, the idea of introduced parameters and the technique of real analysis, a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of the more accurate Hardy–Hilbert’s inequality. An equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.

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