Riesz potential

In mathematics, the Riesz potential is a potential named after its discoverer, the Hungarian mathematician Marcel Riesz. In a sense, the Riesz potential defines an inverse for a power of the Laplace operator on Euclidean space. They generalize to several variables the Riemann–Liouville integrals of one variable.

If 0 < α < n, then the Riesz potential I_αf of a locally integrable function f on Rⁿ is the function defined by

${\displaystyle (I_{\alpha }f)(x)={\frac {1}{c_{\alpha }}}\int _{{\mathbb {R} }^{n}}{\frac {f(y)}{|x-y|^{n-\alpha }}}\,\mathrm {d} y}$

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