Sharp Adams Type Inequalities for the Fractional Laplace–Beltrami Operator on Noncompact Symmetric Spaces

We establish sharp Adams type inequalities on Sobolev spaces \(W^{\alpha , n/\alpha }(X)\) $W^{\alpha ,n/\alpha }(X)$ of any fractional order \(\alpha < n\) $\alpha <n$ on Riemannian symmetric space X of noncompact type with dimension n and of arbitrary rank. We also establish sharp Hardy–Adams inequalities on the Sobolev spaces \(W^{n/2, 2}(X)\) $W^{n/2,2}(X)$ . We use Fourier analysis on the symmetric spaces to obtain these results.