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

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

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￣[1].