Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 89134, 9 pages
doi:10.1155/JIA/2006/89134

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

Abstract

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.