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arXiv · 2305.09279

Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms

Maciej Kucharski·Błażej Wróbel·Jacek Zienkiewicz
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Abstract

We prove a dimension-free $L^p(\mathbb{R}^d)$, $1<p<\infty$, estimate for the vector of higher order maximal Riesz transforms in terms of the corresponding Riesz transforms. This implies a dimension-free $L^p(\mathbb{R}^d)$ estimate for the vector of maximal Riesz transforms in terms of the input function. We also give explicit estimates for the dependencies of the constants on $p$ when the order is fixed. Analogous dimension-free estimates are also obtained for single higher order Riesz transforms with an improved estimate of the constants.

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Maciej Kucharski, Błażej Wróbel, Jacek Zienkiewicz. 2023-06-22. Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms. https://doi.org/10.2140/apde.2026.19.627

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