Bourgain-Brezis-Mironescu formula for Riesz Potentials

Alejandro Claros, Carlos Pérez

We identify the Bourgain-Brezis-Mironescu pointwise limit of the nonlocal potential operator $(1-\hat{I}\pm )I_{\hat{I}}\pm ({\mathcal{D}}^{\hat{I}}\pm f)$, $0<\hat{I}\pm <1$, where $I_{\hat{I}}\pm$ denotes the Riesz potential and…