Riesz Potential

The Riesz potential of order is the integral operator

defined whenever the integral converges, where is the Euclidean norm. It is a convolution with a power-law integral kernel. The normalization constant is chosen so that, for a Schwartz function and the Fourier transform convention using , its Fourier multiplier is , with the identity understood in the sense of generalized functions.

For with and , this is the inverse potential associated with the fractional Laplacian (Mei and Wei 2026).