  In this note we prove that the ball is a maximiser of some Schatten $p$-norms
of the Riesz potential operators among all domains of a given measure in
$\mathbb R^{d}$. In particular, the result is valid for the polyharmonic Newton
potential operator, which is related to a nonlocal boundary value problem for
the poly-Laplacian extending the one considered by M. Kac in the case of the
Laplacian, so we obtain and isoperimetric inequalities for its eigenvalues as
well, namely, analogues of Rayleigh-Faber-Krahn and Hong-Krahn-Szeg\"o
inequalities.
