Communications in Mathematical Analysis

On a Hilbert-Type Inequality with a Hypergeometric Function

Bing He and Bicheng Yang

Full-text: Open access


By applying the method of weight function and techniques from Real Analysis, a Hilbert-type inequality depending upon a multi-parameter with a best constant factor is studied. The best constant is formulated in terms of a hypergeometric function. Furthermore, the inverse inequality is studied.

Article information

Commun. Math. Anal., Volume 9, Number 1 (2010), 84-92.

First available in Project Euclid: 21 April 2010

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26D15

Hilbert's inequality Weight coefficient Hölder's inequality


He , Bing; Yang , Bicheng. On a Hilbert-Type Inequality with a Hypergeometric Function. Commun. Math. Anal. 9 (2010), no. 1, 84--92.

Export citation


  • G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities. Cambridge University Press, 1934.
  • D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives. Kluwer Academic, Boston, 1991.
  • M. Gao, On Hilbert's inequality and its applications. J. Math. Anal. Appl. 212 (1997), pp 316-323.
  • B. G. Pachpatte, Inequalities similar to the integral analogue of Hilbert's inequality. Tamkang J. Math. 30(1999), pp 139-146.
  • B. Yang, The Norm of Operator and Hilbert-type Inequalities. Science Press, Beijing, 2009.
  • B. Yang, On a relation between Hilbert!-s inequality and a Hilbert-type inequality. Appl. Math. Lett., 21(5)(2008), pp 483-488.
  • W. Zhong, A reverse Hilbert's type integral inequality. Internat. J. Pure Appl. Math. 36(3)(2007), pp 353-360.
  • C. Zhao and L. Debnath, Some new inverse type Hilbert integral inequalities. J. Math. Anal. Appl., 262(1)(2001), pp 411-418.
  • Q. Huang, A Hilbert-type Series Inequality with the Homogeneous Kernel of 0-degree. J. Guangdong Edu. Inst., 29(5)(2009), pp 20-23.
  • E.D. Rainville, Special Functions. Chelsea Publishing Co., Bronx, N,Y., 1971.
  • Z. Wang and D. Guo, Introduction to Special Functions. Science Press, Beijing, 1979.
  • J. Kuang, Applied Inequalities, Shangdong Science Press, Jinan, 2004.