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On a multidimensional version of the Hilbert type inequality
Analysis Mathematica, 2012The main objective of this paper is a study of some new multidimensional Hilbert-type inequalities with a general homogeneous kernel. We derive a pair of equivalent inequalities, and also establish the conditions under which the constant factors included in obtained inequalities are the best possible.
Vuković, Predrag, Krnić, Mario
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A Multidimensional Integral Inequality Related to Hilbert-Type Inequality
Mediterranean Journal of Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adiyasuren, Vandanjav +2 more
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A Reverse Hilbert's Type Inequality
Applied Mechanics and Materials, 2014In this paper, by using the Euler-Maclaurin expansion, we establish an inequality of a weight coefficient. Using this inequality, we derive a reverse Hilbert's type inequality. As applications, an equivalent form is obtained.
Gao Wen Xi, Yue Xi, Lei Wang
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An Operator Inequality Related to Hilbert's Type Inequality
Journal of Interdisciplinary Mathematics, 2014AbstractUsing the weight coefficient and the theory of operators, we define a new Hilbert-type operator and obtain its norm. At last, equivalent inequalities with the best constant factor and some particular norms are considered for applications.
Biao Xu, Guang-Sheng Chen
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2009
In this talk we give some new generalizations of classical Hilbert's inequality. We extend it to a general case with $k\geq 2$ non-conjugate exponents. The established technique is then applied to the case where functions are defined $R^n$, and in the case of conjugate exponents and some special homogeneous kernels it is shown that the obtained ...
Perić, Ivan +2 more
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In this talk we give some new generalizations of classical Hilbert's inequality. We extend it to a general case with $k\geq 2$ non-conjugate exponents. The established technique is then applied to the case where functions are defined $R^n$, and in the case of conjugate exponents and some special homogeneous kernels it is shown that the obtained ...
Perić, Ivan +2 more
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Hilbert-Type Integral Inequalities
2009Hilbert-type integral inequalities, including the well known Hilbert’s integral inequality published in 1908, are important in analysis and its applications. This well organized handbook covers the newest methods of weight functions and most important recent results of Hilbert-type integral inequalities and applications in three classes ...
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On a Hilbert-Type Integral Inequality
2011By introducing some parameters and using the way of weight function, a new Hilbert-type integral inequality with a combination kernel is given, which is a best extension of Hilbert’s integral inequality. As applications, the equivalent form is considered.
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On Reverse Hilbert Type Inequalities
2010In this paper we establish a new inverse inequality of Hilbert type for a finite number of positive sequences of real numbers. The integral analogue of the inequality are also proved. The results of this paper reduce to that of B. G. Pachpatte.
Bencze, M, Zhou, C, Cheung, WS
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Extension of Hilbert's inequality
Journal of Mathematical Analysis and Applications, 2006Josip Pecaric, Mario Krnic
exaly
On Some New Inequalities Similar to Hilbert's Inequality
Journal of Mathematical Analysis and Applications, 1998B G Pachpatte
exaly