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arXiv · 2403.00173

Kernel Smoothing Operators on Thick Open Domains

Dimitrios Giannakis·Mohammad Javad Latifi Jebelli
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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.

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Dimitrios Giannakis, Mohammad Javad Latifi Jebelli. 2024-02-29. Kernel Smoothing Operators on Thick Open Domains. https://arxiv.org/abs/2403.00173

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