  We give a proof that the first eigenfunction of the $\alpha$-symmetric stable
process on a bounded Lipschitz domain in $\R^d$, $d\geq 1$, is superharmonic
for $\alpha=2/m$, where $m>2$ is an integer. This result was first proved for
the ball by M. Ka{\ss}mann and L. Silvestre (personal communication) with
different methods. For $\alpha=1$, the result was proved in \cite[Theorem
4.7]{BanKul}.
