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Journal of Function Spaces and Applications
Volume 1, Issue 1, Pages 1-15
http://dx.doi.org/10.1155/2003/860547

Hardy operator with variable limits on monotone functions

1Department of Mathematics, KAIST, 373-1 Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of Korea
2Computing Centre FEB RAS, Tikhookeanskaya 153, Khabarovsk, 680042, Russia

Received 1 February 2003

Academic Editor: Lars-Erik Persson

Copyright © 2003 Hindawi Publishing Corporation. 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.

Abstract

We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=a(x)b(x)f(y)u(y)dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits.