Riesz potential

In mathematics, a Riesz potential is a scalar function $V\_\{alpha\}\; :\; mathbb\{R\}^\{n\}\; o\; mathbb\{R\}$, $n\; geq\; 2$, of the form

:$V\_\{alpha\}\; (x)=\; int\_$mathbb{R^n} frac{1}{| x - y |^{alpha , mathrm{d} mu (y),

where $alpha\; >\; 0$ and $mu$ is a Borel measure whose support is a compact subset of $mathbb\{R\}^\{n\}$. When $n\; geq\; 3$ and $alpha\; =\; n\; -\; 2$, the Riesz potential coincides with the Newtonian potential.

The Riesz potential is named after the Hungarian mathematician Marcel Riesz.

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