Open Access

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

Journal of Inequalities and Applications20072008:475957

DOI: 10.1155/2008/475957

Received: 12 February 2007

Accepted: 9 November 2007

Published: 27 November 2007

Abstract

We use the potential theory to give integral representations of functions in the Sobolev spaces , where and is a smooth bounded domain in . As a byproduct, we obtain sharp inequalities of Ostrowski type.

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Authors’ Affiliations

(1)
Department of Mathematics, Australian National University
(2)
School of Computer Science and Mathematics, Victoria University

Copyright

© F. C. Cîrstea and S. S. Dragomir. 2008

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.