Kernel Smoothing Operators on Thick Open Domains

Abstract

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.

arXiv comment28 pages, 5 figures