Abstract and Applied Analysis
Volume 2013 (2013), Article ID 904721, 7 pages
Research Article

Some Inequalities for Multiple Integrals on the -Dimensional Ellipsoid, Spherical Shell, and Ball

1College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Autonomous Region, Tongliao City 028043, China
2Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City 300387, China
3School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China

Received 11 January 2013; Accepted 28 February 2013

Academic Editor: Josip E. Pečarić

Copyright © 2013 Yan Sun et al. 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.


The authors establish some new inequalities of Pólya type for multiple integrals on the -dimensional ellipsoid, spherical shell, and ball, in terms of bounds of the higher order derivatives of the integrands. These results generalize the main result in the paper by Feng Qi, Inequalities for a multiple integral, Acta Mathematica Hungarica (1999).