Adams inequalities with exact growth condition for Riesz-like potentials on $\mathbb{R}^n$

Abstract: We derive sharp Adams inequalities with exact growth condition for the Riesz potential as well as more general Riesz-like potentials on R^n. We also obtain Moser-Trudinger inequalities with exact growth condition for the fractional Laplacian, and for general homogeneous elliptic differential operators with constant coefficients.