|
|||||
 |
|
|
|
|
|
|
|
Dimension-free $L^p$
estimates for higher-order maximal Riesz transforms in terms
of the Riesz transforms
Maciej Kucharski, Błażej Wróbel and Jacek Zienkiewicz |
|
Vol. 19 (2026), No. 4, 627–657
|
 |
Abstract |
|
We prove a dimension-free estimate, , for the vector of higher-order maximal Riesz transforms in terms of the corresponding Riesz transforms. This implies a dimension-free 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 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. |
Keywords
higher-order Riesz transform, maximal function,
dimension-free estimates
|
Mathematical Subject Classification
Primary: 42B15, 42B20, 42B25
|
Milestones
Received: 8 December 2023
Revised: 8 May 2025
Accepted: 8 June 2025
Published: 17 May 2026
|
Authors |
| Maciej Kucharski | |
| Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland |
|
| Błażej Wróbel | |
| Instytut Matematyczny Polskiej
Akademii Nauk Warsaw Poland |
Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland |
| Jacek Zienkiewicz | |
| Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland |
|
| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
