Open Access

Global integrability of the Jacobian of a composite mapping

Journal of Inequalities and Applications20062006:89134

DOI: 10.1155/JIA/2006/89134

Received: 18 September 2005

Accepted: 24 October 2005

Published: 27 April 2006

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Seattle University
(2)
Department of Mathematical Sciences, University Center, Saginaw Valley State University

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Copyright

© S. Ding and B. Liu. 2006

This article is published under license to BioMed Central Ltd. 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.