Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on [formula omitted

Abstract

We derive sharp Adams inequalities for the Riesz and more general Riesz-like potentials on the whole of Rn. As a consequence, we obtain sharp Moser–Trudinger inequalities for the critical Sobolev spaces Wα,nα(Rn), 0<α<n. These inequalities involve fractional Laplacians, higher order gradients, general homogeneous elliptic operators with constant coefficients, and general trace type Borel measures.