An Improved Discrete Hardy Inequality

Abstract

In this note, we prove an improvement of the classical discrete Hardy inequality. Our improved Hardy-type inequality holds with a weight w which is strictly greater than the classical Hardy weight w_H(n) ≔ 1/(2n)², where .

MSC:

• Primary 26D15

Acknowledgments

M. K. acknowledges the financial support of the German Science Foundation. Y. P. and F. P. acknowledge the support of the Israel Science Foundation (grants no. 970/15) founded by the Israel Academy of Sciences and Humanities. Furthermore, F. P. is grateful for support through a Technion Fine Fellowship.