Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 89134, 9 pages

Global integrability of the Jacobian of a composite mapping

Shusen Ding1 and Bing Liu2

1Department of Mathematics, Seattle University, Seattle 98122, WA, USA
2Department of Mathematical Sciences, Saginaw Valley State University, University Center, 48710, MI, USA

Received 18 September 2005; Accepted 24 October 2005

Copyright © 2006 Shusen Ding and Bing Liu. 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.


We first obtain an improved version of the Hölder inequality with Orlicz norms. Then, as an application of the new version of the Hölder inequality, we study the integrability of the Jacobian of a composite mapping. Finally, we prove a norm comparison theorem.