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arXiv · 2105.10519

A dimension-free estimate on $L^2$ for the maximal Riesz transform in terms of the Riesz transform

Maciej Kucharski·Błażej Wróbel
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Abstract

W prove a dimension-free estimate for the $L^2(\mathbb{R}^d)$ norm of the maximal truncated Riesz transform in terms of the $L^2(\mathbb{R}^d)$ norm of the Riesz transform. Consequently, the vector of maximal truncated Riesz transforms has a dimension-free estimate on $L^2(\mathbb{R}^d)$. We also show that the maximal function of the vector of truncated Riesz transforms has a dimension-free estimate on all $L^p(\mathbb{R}^d)$ spaces, $1<p<\infty.$

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Maciej Kucharski, Błażej Wróbel. 2021-05-21. A dimension-free estimate on $L^2$ for the maximal Riesz transform in terms of the Riesz transform. https://arxiv.org/abs/2105.10519

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