Abstract:
For general Carnot groups, we obtain coercive estimates for homogeneous
di erential operators with constant coe cients, kernels of which have nite dimension.
We develop new Sobolev-type integral representations of di erentiable functions
which are a crucial tool for deriving coercive estimates. Moreover we prove some auxiliary
results having independent interest, in particular, Sobolev type embedding and
compactness theorems for John domains.
