Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 212915, 13 pages
doi:10.1155/2009/212915
Research Article

Norm Comparison Inequalities for the Composite Operator

Yuming Xing1 and Shusen Ding2

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Seattle University, Seattle, WA 98122, USA

Received 2 August 2008; Accepted 15 January 2009

Academic Editor: András Rontó

Copyright © 2009 Yuming Xing and Shusen Ding. 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 establish norm comparison inequalities with the Lipschitz norm and the BMO norm for the composition of the homotopy operator and the projection operator applied to differential forms satisfying the A-harmonic equation. Based on these results, we obtain the two-weight estimates for Lipschitz and BMO norms of the composite operator in terms of the Ls-norm.