  We consider the Dirichlet-to-Neumann operator ${\cal N}$ associated with a
general elliptic operator \[ {\cal A} u = - \sum_{k,l=1}^d \partial_k (c_{kl}\,
\partial_l u) + \sum_{k=1}^d \Big( c_k\, \partial_k u - \partial_k (b_k\, u)
\Big) +c_0\, u \in {\cal D}'(\Omega) \] with possibly complex coefficients. We
study three problems:
  1) Boundedness on $C^\nu$ and on $L_p$ of the commutator $[{\cal N}, M_g]$,
where $M_g$ denotes the multiplication operator by a smooth function $g$.
  2) H\"older and $L_p$-bounds for the harmonic lifting associated with ${\cal
A}$.
  3) Poisson bounds for the heat kernel of ${\cal N}$.
  We solve these problems in the case where the coefficients are H\"older
continuous and the underlying domain is bounded and of class $C^{1+\kappa}$ for
some $\kappa > 0$. For the Poisson bounds we assume in addition that the
coefficients are real-valued. We also prove gradient estimates for the heat
kernel and the Green function $G$ of the elliptic operator with Dirichlet
boundary conditions.
