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

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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Correspondence to Sever S. Dragomir.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cîrstea, F.C., Dragomir, S.S. Representation of Multivariate Functions via the Potential Theory and Applications to Inequalities. J Inequal Appl 2008, 475957 (2007). https://doi.org/10.1155/2008/475957

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Keywords

  • Potential Theory
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  • Multivariate Function
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