Open Access

Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator

Journal of Inequalities and Applications20052005:374053

DOI: 10.1155/JIA.2005.387

Received: 3 November 2003

Published: 31 August 2005

Abstract

We consider and a corresponding geometric mean operator . E. T. Sawyer showed that the Hardy-type inequality could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight is of product type, then in fact only one condition is needed. Moreover, by using this information and by performing a limiting procedure we can derive a weight characterization of the corresponding two-dimensional Pólya-Knopp inequality with the geometric mean operator involved.

Authors’ Affiliations

(1)
Department of Mathematics, Luleå University

Copyright

© Wedestig. 2005