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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.19032 |
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Table of Contents:
- We study the frequency function (introduced by Temur) in both the discrete and continuous settings. More precisely, we extend the definition of the frequency function to the higher-dimensional continuous setting and to the uncentered Hardy-Littlewood maximal function. We analyze the asymptotic behavior of the frequency function and the density of its small values for functions in $\ell^1(\mathbb{Z)}$ and $L^1(\mathbb{R}^d)$ answering some questions posed by Temur. Finally, we study the size of the frequency function for functions in $\ell^p(\mathbb{Z})$ with $p>1$, showing that this case differs significantly from the case $p=1$.