On a Bilateral Hilbert-Type Inequality with a Homogeneous Kernel of 0-Degree

- Journal title : Kyungpook mathematical journal
- Volume 50, Issue 2, 2010, pp.307-314
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2010.50.2.307

Title & Authors

On a Bilateral Hilbert-Type Inequality with a Homogeneous Kernel of 0-Degree

He, Bing;

He, Bing;

Abstract

By introducing a homogeneous kernel of 0-degree with an independent parameter and estimating the weight coefficient, a bilateral form of the Hilbert-type series inequality with a best constant factor is established.

Keywords

Hilbert's inequality;Weight coefficient;Hlder's inequality;

Language

English

Cited by

References

1.

G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1934.

2.

D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic, Boston, 1991.

4.

J. Kuang, On new extensions of Hilbert's integral inequality, Math. Anal. Appl., 235(1999), 608-614.

5.

B. G. Pachpatte, Inequalities similar to the integral analogue of Hilbert's inequality, Tamkang J. Math., 30(1999), 139-146.

6.

B. Yang, The Norm of Operator and Hilbert-type Inequalities, Science Press, Beijing, 2009.

7.

B. Yang, On a relation between Hilberts inequality and a Hilbert-type inequality, Applied Mathematics Letters, 21, 5(2008), 483-488.

8.

W. Zhong and B. Yang, A reverse form of multiple Hardy-Hilbert's integral inequality, International Journal of Mathematical Inequalities and Applications, 2007, 1(1), 67- 72.

9.

C. Zhao and L. Debnath, Some new inverse type Hilbert integral inequalities, Journal of Mathematical Analysis and Applications, 2001, 262(1), 411-418.

10.

J. Kuang, Applied Inequalities, Shangdong Science Press, Jinan, 2004.