Following our preceding papers devoted to the case of general Hörmander’s operators
with analytic-Gevrey
coefficients on an open set
in
,
for which we established local relations of domination by powers of
and derived from it
local
-Gevrey regularity
of local
-Gevrey vectors
of
(with, furthermore,
suitable relations between
and the coefficient of the Sobolev estimate satisfied by
), this
article deals with the case of Hörmander’s operators of first kind (or of degenerate elliptic
kind). We establish, in this case, precise local relations of domination by powers of
which give, when
applied to the
-Gevrey
regularity of
-Gevrey
vectors of
,
in
, with
, an optimal relation
between
and the
type of
with respect
to the system
of vector fields whose sum of squares is the leading part of
.
