Good morning everybody.
I was looking just for a quick reference to know whether the Dirichlet problem has a solution in the Heisenberg group, that is $\mathbb R^3$ endowed with coordinates $(x,y,z)$ and an horizontal distribution spanned by $X=\partial_x-\frac y2\partial_z$ and $Y=\partial_y+\frac x2 \partial_z$.
I don't look for representation formulas, rather to the standard existence results like harnack maximum principles, etc..
Many thanks in advance.
Regards, Guido