Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 475957, 15 pages
Representation of Multivariate Functions via the Potential Theory and Applications to Inequalities
1Department of Mathematics, Australian National University, Canberra, ACT 0200, Australia
2School of Computer Science and Mathematics, Victoria University, P.O. Box 14428, Melbourne City, Victoria 8001, Australia
Received 12 February 2007; Revised 2 August 2007; Accepted 9 November 2007
Academic Editor: Siegfried Carl
Copyright © 2008 Florica C. Cîrstea and Sever S. Dragomir. 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 use the potential theory to give integral representations of functions
in the Sobolev spaces , where
is a smooth bounded domain in .
As a byproduct, we obtain sharp inequalities of Ostrowski type.