Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 475957, 15 pages
doi:10.1155/2008/475957
Research Article

Representation of Multivariate Functions via the Potential Theory and Applications to Inequalities

Florica C. Cîrstea1 and Sever S. Dragomir2

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.

Abstract

We use the potential theory to give integral representations of functions in the Sobolev spaces W1,p(Ω), where p≥1 and Ω is a smooth bounded domain in ℝN (N≥2). As a byproduct, we obtain sharp inequalities of Ostrowski type.