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  • Research Article
  • Open Access

Global integrability of the Jacobian of a composite mapping

Journal of Inequalities and Applications20062006:89134

  • Received: 18 September 2005
  • Accepted: 24 October 2005
  • Published:


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.


  • Comparison Theorem
  • Composite Mapping
  • Global Integrability
  • Norm Comparison
  • Orlicz Norm


Authors’ Affiliations

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


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© 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.