Kernel Smoothing Operators on Thick Open Domains

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