Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 179-185.

• Articles • Previous Articles     Next Articles

A Generalization of Hilbert-type Integral Inequality

 LIU Qiong, LONG Shun-Chao   

  1. Department of Science and Information, Shaoyang University, Hunan Shaoyang 422000; Deptartment of Mathematics, Xiangtan University, Hunan Xiangtan |411105
  • Received:2012-05-12 Revised:2013-07-09 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金项目(11171280)和湖南省教育厅科学项目(10C1186)资助.

Abstract:

By introducing Γ-function and ζ-function, and using the way of weight function and the method of real analysis, a generalized Hilbert-type integral inequality is given. The equivalent form is considered and their constant factors are proved being the best possible. By taking the special parameter values, some meaningful results are obtained.

Key words: Hilbert-type integral inequality, Weight function, The best constant factor,  Γ-function,  ζ-function, H\"{o}lder’s inequality, Results

CLC Number: 

  • 26D15
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