Skip to content


  • Research Article
  • Open Access

A Multiple Hilbert-Type Integral Inequality with the Best Constant Factor

Journal of Inequalities and Applications20072007:071049

  • Received: 9 February 2007
  • Accepted: 29 April 2007
  • Published:


By introducing the norm and two parameters , , we give a multiple Hilbert-type integral inequality with a best possible constant factor. Also its equivalent form is considered.


  • Constant Factor
  • Equivalent Form
  • Integral Inequality


Authors’ Affiliations

Zhejiang Water Conservancy and Hydropower College, Zhejiang University, Hangzhou, 310018, China


  1. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, Cambridge, UK; 1952:xii+324.MATHGoogle Scholar
  2. Mitrinović DS, Pečarić JE, Fink AM: Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and Its Applications (East European Series). Volume 53. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1991:xvi+587.View ArticleGoogle Scholar
  3. Gao M, Yang B: On the extended Hilbert's inequality. Proceedings of the American Mathematical Society 1998,126(3):751–759. 10.1090/S0002-9939-98-04444-XMathSciNetView ArticleMATHGoogle Scholar
  4. Jichang K, Debnath L: On new generalizations of Hilbert's inequality and their applications. Journal of Mathematical Analysis and Applications 2000,245(1):248–265. 10.1006/jmaa.2000.6766MathSciNetView ArticleMATHGoogle Scholar
  5. Jichang K: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.Google Scholar
  6. Pachpatte BG: On some new inequalities similar to Hilbert's inequality. Journal of Mathematical Analysis and Applications 1998,226(1):166–179. 10.1006/jmaa.1998.6043MathSciNetView ArticleMATHGoogle Scholar
  7. Yang B, Debnath L: On new strengthened Hardy-Hilbert's inequality. International Journal of Mathematics and Mathematical Sciences 1998,21(2):403–408. 10.1155/S0161171298000556MathSciNetView ArticleMATHGoogle Scholar
  8. Yang B: On a general Hardy-Hilbert's integral inequality with a best constant. Chinese Annals of Mathematics. Series A 2000,21(4):401–408.MathSciNetMATHGoogle Scholar
  9. Yang B: On a generalization of a Hilbert's type integral inequality and its applications. Mathematica Applicata 2003,16(2):82–86.MathSciNetMATHGoogle Scholar
  10. Hong Y: All-sided generalization about Hardy-Hilbert integral inequalities. Acta Mathematica Sinica. Chinese Series 2001,44(4):619–626.MathSciNetMATHGoogle Scholar
  11. Yang B: A multiple Hardy-Hilbert integral inequality. Chinese Annals of Mathematics. Series A 2003,24(6):743–750.MathSciNetMATHGoogle Scholar
  12. Yong H: A multiple Hardy-Hilbert integral inequality with the best constant factor. Journal of Inequalities in Pure and Applied Mathematics 2006,7(4, article 139):10.MathSciNetGoogle Scholar
  13. Hua L: An Introduction to Advanced Mathematics (Remaining Sections). Science Publishers, Beijing, China; 1984.Google Scholar