In our main result
we shall
consider an hypoelliptic linear partial differential operator

with

coefficients defined on an open set

and
consider a solution

of the equation

which extends to a distribution
defined in a neighborhood of some point

in the boundary

of

.
If hypoellipticity is a consequence of the existence of a suitable right
parametrix of pseudodifferential type,
then we shall show that

must have temperate growth at the boundary near

.