Representation of multivariate functions via the potential theory and applications to inequalities

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Abstract

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

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Cǐrstea, F. C., & Dragomir, S. S. (2008). Representation of multivariate functions via the potential theory and applications to inequalities. Journal of Inequalities and Applications, 2008. https://doi.org/10.1155/2008/475957

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