Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 357-367

A weighted inequality for derivatives on the half-line

T. Kilgore

Mathematics, Auburn University, Auburn 36849-5307, Alabama, USA

Received 12 January 1997

Copyright © 1997 T. Kilgore. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some inequalities will be presented, which give weighted norm estimates for derivatives of functions defined on the half-line. These inequalities are related to Hardy’s inequality, and they also generalize Hardy’s inequality to higher derivatives. The results presented here are also analogous to some recently-derived inequalities for the derivatives of functions defined on the interval [1,1], which have had important applications to the study of polynomial approximation on [1,1].