Hardy－Riesz拓广了的Hilbert不等式的一个改进

An Improvement of Hardy-Riesz’s Extension of the Hilbert Ineqnality

中文关键词:  Steffensen不等式  Euler－Maclaurin求和公式  单调函数  Hilbcrt不等式。

中文摘要:

      本文利用Ｅｕｌｅｒ－Ｍａｃｌａｕｒｉｎ求和公式以及Ｓｔｃｆｆｃｎｓｃｎ不等式改进了文［１］的结果。

英文摘要:

      In this paper, using Steffensen’s integral inequality and the summation formula ofEuler-Mac- laurin, we prove that the following inequality is valid: where p > 1 is a real number, and n is an arbitrary positive integer. Using this result, wegive a refinement on the result given recently by L. C. Hsu and Guo Yongkang.