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

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We 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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Authors and Affiliations

  1. Instytut Matematyczny, Uniwersytet Wrocławski, Plac Grunwaldzki 2, 50–384, Wrocław, Poland

    Maciej Kucharski & Błażej Wróbel

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  1. Maciej Kucharski
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  2. Błażej Wróbel
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Correspondence to Błażej Wróbel.

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Both authors were supported by the National Science Centre (NCN), Poland research project Preludium Bis 2019/35/O/ST1/00083.

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Kucharski, M., Wróbel, B. A dimension-free estimate on \(L^2\) for the maximal Riesz transform in terms of the Riesz transform. Math. Ann. 386, 1017–1039 (2023). https://doi.org/10.1007/s00208-022-02417-5

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