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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 628250, 8 pages
http://dx.doi.org/10.1155/2013/628250
Research Article

A More Accurate Half-Discrete Hilbert Inequality with a Nonhomogeneous Kernel

Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Received 8 May 2013; Accepted 3 June 2013

Academic Editor: Kehe Zhu

Copyright © 2013 Qiliang Huang and Bicheng Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Weyl, Singulare integral gleichungen mit besonderer berucksichtigung des fourierschen integral theorems [Inaugeral-Dissertation], Gottingen, 1908.
  2. I. Schur, “Bernerkungen sur Theorie der beschrankten Bilinearformen mit unendlich vielen veranderlichen,” Journal für die Reine und Angewandte Mathematik, vol. 140, pp. 1–28, 1911. View at Google Scholar
  3. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Acaremic, Boston, Mass, USA, 1991.
  4. Y. Bicheng, “On Hilbert's Integral Inequality,” Journal of Mathematical Analysis and Applications, vol. 220, no. 2, pp. 778–785, 1998. View at Publisher · View at Google Scholar · View at Scopus
  5. B. Yang and L. Debnath, “On the extended Hardy-Hilbert's inequality,” Journal of Mathematical Analysis and Applications, vol. 272, no. 1, pp. 187–199, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Jin and L. Debnath, “On a Hilbert-type linear series operator and its applications,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 691–704, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. B. Yang and T. M. Rassias, “On a new extension of Hilbert's inequality,” Mathematical Inequalities and Applications, vol. 8, no. 4, pp. 575–582, 2005. View at Google Scholar · View at Scopus
  8. M. Krnić and J. Pečarić, “Hilbert's inequalities and their reverses,” Publicationes Mathematicae Debrecen, vol. 67, no. 3-4, pp. 315–331, 2005. View at Google Scholar
  9. L. E. Azar, “On some extensions of hardy-hilbert's inequality and applications,” Journal of Inequalities and Applications, vol. 2008, Article ID 546829, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. Q. Huang and B. Yang, “On a multiple hilbert-type integral operator and applications,” Journal of Inequalities and Applications, vol. 2009, Article ID 192197, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. Q. Huang, “On a Multiple hilbert's inequality with parameters,” Journal of Inequalities and Applications, vol. 2010, Article ID 309319, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. B. Yang, The Norm of Operator and Hilbert-Type Inequalities, Science Press, Beijing, China, 2009 (Chinese).
  13. B. Yang, Hilbert-Type Integral Inequalities, Bentham Science, Dubai, UAE, 2009.
  14. B. Yang, Discrete Hilbert-Type Inequalities, Bentham Science, Dubai, UAE, 2011.
  15. J. Kuang, Applied Inequalities, Shangdong Science Technic Press, Jinan, China, 2010 (Chinese).
  16. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, UK, 1934.
  17. B. Yang, “A mixed Hilbert-type inequality with a best constant factor,” International Journal of Pure and Applied Mathematics, vol. 20, no. 3, pp. 319–328, 2005. View at Google Scholar
  18. B. Yang, “On a half-discrete reverse hilbert-yype inequality with a non-homogeneous kernel,” Journal of Inner Mongolia Normal University (Natural Science Edition), vol. 40, no. 5, pp. 433–436, 2011 (Chinese). View at Google Scholar