Dimension-free estimates for positivity-preserving Riesz transforms related to Schrödinger operators with certain potentials
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910432350961664 |
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| author | Kucharski, Maciej |
| author_facet | Kucharski, Maciej |
| contents | We study the $L^\infty(\mathbb{R}^d)$ boundedness for Riesz transforms of the form ${V^{a}(-\frac12Δ+V)^{-a}},$ where $a > 0$ and $V$ is a non-negative potential with power growth acting independently on each coordinate. We factorize the semigroup $e^{-tL}$ into one-dimensional factors, estimate them separately and combine the results to estimate the original semigroup. Similar results with additional assumption $a \leqslant 1$ are obtained on $L^1(\mathbb{R}^d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension-free estimates for positivity-preserving Riesz transforms related to Schrödinger operators with certain potentials Kucharski, Maciej Functional Analysis 47D08, 42B20, 42B37 We study the $L^\infty(\mathbb{R}^d)$ boundedness for Riesz transforms of the form ${V^{a}(-\frac12Δ+V)^{-a}},$ where $a > 0$ and $V$ is a non-negative potential with power growth acting independently on each coordinate. We factorize the semigroup $e^{-tL}$ into one-dimensional factors, estimate them separately and combine the results to estimate the original semigroup. Similar results with additional assumption $a \leqslant 1$ are obtained on $L^1(\mathbb{R}^d)$. |
| title | Dimension-free estimates for positivity-preserving Riesz transforms related to Schrödinger operators with certain potentials |
| topic | Functional Analysis 47D08, 42B20, 42B37 |
| url | https://arxiv.org/abs/2405.01415 |