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. ( I α f ) ( x ) = 1 c α ∫ R n f ( y ) | x − y | n − α d y {displaystyle (I_{alpha }f)(x)={frac {1}{c_{alpha }}}int _{{mathbb {R} }^{n}}{frac {f(y)}{|x-y|^{n-alpha }}},mathrm {d} y}     (1) 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 Iαf of a locally integrable function f on Rn is the function defined by