  We define the notion of a thick open set $\Omega$ in a Euclidean space and
show that a local Hardy-Littlewood inequality holds in $L^p(\Omega)$, $p \in
(1, \infty]$. We then establish pointwise and $L^p(\Omega)$ convergence for
families of convolution operators with a Markov normalization on $\Omega$. We
demonstrate application of such smoothing operators to piecewise-continuous
density, velocity, and stress fields from discrete element models of sea ice
dynamics.
