  We show that the dominating set problem admits a constant factor
approximation in a constant number of rounds in the LOCAL model of distributed
computing on graph classes with bounded expansion. This generalizes a result of
Czygrinow et al. for graphs with excluded topological minors to very general
classes of uniformly sparse graphs. We demonstrate how our general algorithm
can be modified and fine-tuned to compute an ($11+\epsilon$)-approximation (for
any $\epsilon>0)$ of a minimum dominating set on planar graphs. This improves
on the previously best known approximation factor of 52 on planar graphs, which
was achieved by an elegant and simple algorithm of Lenzen et al.
