Dirichlet problem in the class of $s{{h}_{m}}$-functions on manifold $X$

In the talk we consider the solvability of the Dirichlet problem in the class of $s{{h}_{m}}$-functions on the Stein manifold $X\subset {{\mathbb{C}}^{N}}$, $\dim X=n$. Also we consider the functional properties of the solution of the Dirichlet problem.