Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.13019 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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).