Journal of Inequalities and Applications 
Volume 1 (1997), Issue 4, Pages 357-367
doi:10.1155/S1025583497000258

A weighted inequality for derivatives on the half-line

T. Kilgore

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

Received 12 January 1997

Abstract

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].