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