Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

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

  • He, Bing (Department of Mathematics, Guangdong Education College)
  • Received : 2009.10.21
  • Accepted : 2010.01.27
  • Published : 2010.06.30
Download PDF
⟨ Previous Next ⟩

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

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.
  3. M. Gao, On Hilbert's inequality and its applications, J. Math. Anal. Appl., 212(1997), 316-323. https://doi.org/10.1006/jmaa.1997.5490
  4. J. Kuang, On new extensions of Hilbert's integral inequality, Math. Anal. Appl., 235(1999), 608-614. https://doi.org/10.1006/jmaa.1999.6373
  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. https://doi.org/10.1016/j.aml.2007.06.001
  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. https://doi.org/10.1006/jmaa.2001.7595
  10. J. Kuang, Applied Inequalities, Shangdong Science Press, Jinan, 2004.

Cited by

  1. A new extension of a Hardy-Hilbert-type inequality vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0918-7