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

Abstract:

      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.