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 $L^p(Ω)$, $p \in (1, \infty]$. We then establish pointwise and $L^p(Ω)$ convergence for families of convolution operators with a Markov normalization on $Ω$. We demonstrate ap...
| Main Authors: | , |
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| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
arXiv
2024
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2403.00173 https://arxiv.org/abs/2403.00173 |
| Summary: | We define the notion of a thick open set $Ω$ in a Euclidean space and show that a local Hardy-Littlewood inequality holds in $L^p(Ω)$, $p \in (1, \infty]$. We then establish pointwise and $L^p(Ω)$ 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. ... : 28 pages, 5 figures ... |
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