PreprintCC BY 4.0arXiv
Fefferman-Stein Type Distribution Function Inequalities on Product Spaces
Abstract
We establish on Rn× Rm a Fefferman--Stein type distribution function inequality in which the nontangential maximal function of the product Poisson extension is controlled by the Lusin area integral function: |{N>λ}|≤ C(|{A>λ}|+λ−2∫{A≤λ}A2 dx). The central idea is to establish a local L2 estimate for the radial maximal function. This yields a new proof of the corresponding one-parameter inequality, avoiding Green's formula and the treatment of sawtooth regions, and extends to the multiparameter setting.
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BibTeX
@misc{chen2026feffermanstein,
title = {{Fefferman-Stein Type Distribution Function Inequalities on Product Spaces}},
author = {Jiecheng Chen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.11186},
eprint = {2611.11186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.11186},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fefferman-Stein Type Distribution Function Inequalities on Product Spaces
AU - Jiecheng Chen
PY - 2026
DA - 2026/11/08
PB - arXiv
DO - 10.48550/arxiv.2611.11186
UR - https://arxiv.org/abs/2611.11186
AB - We establish on R^n× R^m a Fefferman--Stein type distribution function inequality in which the nontangential maximal function of the product Poisson extension is controlled by the Lusin area integral function: |{N>λ}|≤ C(|{A>λ}|+λ^−2∫_{A≤λ}A^2 dx). The central idea is to establish a local L^2 estimate for the radial maximal function. This yields a new proof of the corresponding one-parameter inequality, avoiding Green's formula and the treatment of sawtooth regions, and extends to the multiparameter setting.
ER -