Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on Rn

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