PreprintCC BY 4.0arXiv
Shorter proof of dimension-free Lp estimates for maximal Riesz transforms
Abstract
We provide a shorter and more direct proof of Lp estimates for maximal Riesz transforms (of an arbitrary order) in terms of the corresponding Riesz transforms, with a constant independent of the dimension of the Euclidean space ℝd. This result was originally proved by Mateu, Orobitg, Pérez and Verdera with a constant depending on the dimension, and improved to a dimension-free inequality by Kucharski, Wróbel and Zienkiewicz.
Related
- Dimension-free weak (1,1) estimates for Riesz transforms with constant drift
- A direct obstacle proof of a dimension-free weak-type (1,1) bound for the Gaussian Riesz transforms
- Optimal dimension-dependent ℓp and ℓ1,∞ estimates of the second-order discrete Riesz transforms
- Dimension-free estimates for full discrete maximal functions associated with Euclidean balls and spheres
- Dimension-free estimates for the full discrete Euclidean ball maximal function
BibTeX
@misc{kucharski2026shorter,
title = {{Shorter proof of dimension-free $L^p$ estimates for maximal Riesz transforms}},
author = {Maciej Kucharski and Mateusz Kwaśnicki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11537},
eprint = {2609.11537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11537},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shorter proof of dimension-free L^p estimates for maximal Riesz transforms
AU - Maciej Kucharski
AU - Mateusz Kwaśnicki
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.11537
UR - https://arxiv.org/abs/2609.11537
AB - We provide a shorter and more direct proof of L^p estimates for maximal Riesz transforms (of an arbitrary order) in terms of the corresponding Riesz transforms, with a constant independent of the dimension of the Euclidean space ℝ^d. This result was originally proved by Mateu, Orobitg, Pérez and Verdera with a constant depending on the dimension, and improved to a dimension-free inequality by Kucharski, Wróbel and Zienkiewicz.
ER -