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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.13019 |
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| _version_ | 1866918107968176128 |
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| author | Temur, Faruk Özcan, Hikmet Burak |
| author_facet | Temur, Faruk Özcan, Hikmet Burak |
| contents | In a recent short note the first author gave the first positive result on the higher order regularity of the discrete noncentered Hardy-Littlewood maximal function. In this article we conduct a thorough investigation of possible similar results for higher order derivatives. We uncover that such results are indeed a consequence of a stronger phenomenon regarding the growth of $l^p(\Z)$ norms of the derivatives of characteristic functions of finite subsets of $\Z$. Along the way we discover very interesting connections to Prouhot-Tarry-Escott (PTE) problem, and to zeros of complex polynomials with restricted coefficients (Littlewood-type polynomials). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The higher regularity of the discrete Hardy-Littlewood maximal function Temur, Faruk Özcan, Hikmet Burak Classical Analysis and ODEs Primary: 42B25, Secondary: 46E35, 68R05 In a recent short note the first author gave the first positive result on the higher order regularity of the discrete noncentered Hardy-Littlewood maximal function. In this article we conduct a thorough investigation of possible similar results for higher order derivatives. We uncover that such results are indeed a consequence of a stronger phenomenon regarding the growth of $l^p(\Z)$ norms of the derivatives of characteristic functions of finite subsets of $\Z$. Along the way we discover very interesting connections to Prouhot-Tarry-Escott (PTE) problem, and to zeros of complex polynomials with restricted coefficients (Littlewood-type polynomials). |
| title | The higher regularity of the discrete Hardy-Littlewood maximal function |
| topic | Classical Analysis and ODEs Primary: 42B25, Secondary: 46E35, 68R05 |
| url | https://arxiv.org/abs/2504.13019 |