Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917534619402240 |
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| author | Kucharski, Maciej Wróbel, Błażej Zienkiewicz, Jacek |
| author_facet | Kucharski, Maciej Wróbel, Błażej Zienkiewicz, Jacek |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_09279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms Kucharski, Maciej Wróbel, Błażej Zienkiewicz, Jacek Classical Analysis and ODEs Functional Analysis 42B25, 42B20, 42B15 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. |
| title | Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms |
| topic | Classical Analysis and ODEs Functional Analysis 42B25, 42B20, 42B15 |
| url | https://arxiv.org/abs/2305.09279 |