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arXiv · 2405.01415

Dimension-free estimates for positivity-preserving Riesz transforms related to Schr\"odinger operators with certain potentials

Maciej Kucharski
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Abstract

We study the $L^\infty(\mathbb{R}^d)$ boundedness for Riesz transforms of the form ${V^{a}(-\frac12\Delta+V)^{-a}},$ 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 $L^1(\mathbb{R}^d)$.

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Maciej Kucharski. 2024-05-02. Dimension-free estimates for positivity-preserving Riesz transforms related to Schr\"odinger operators with certain potentials. https://arxiv.org/abs/2405.01415

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