  Euler operators are partial differential operators of the form $P(\theta)$
where $P$ is a polynomial and $\theta_j = x_j \partial/\partial x_j$. They are
surjective on the space of temperate distributions on $R^d$. We show that this
is, in general, not true for the space of Schwartz distributions on $R^d$,
$d\ge 3$, for $d=1$, however, it is true. It is also true for the space of
distributions of finite order on $R^d$ and on certain open sets $\Omega\subset
R^d$, like the euclidian unit ball.
