  We prove sharp pointwise heat kernel estimates for symmetric Markov processes
associated with symmetric Dirichlet forms that are local with respect to some
coordinates and nonlocal with respect to the remaining coordinates. The main
theorem is a robustness result like the famous estimate for the fundamental
solution of second order differential operators, obtained by Donald G. Aronson.
Analogous to his result, we show that the corresponding translation-invariant
process and the one given by the general Dirichlet form share the same
pointwise points.
