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arXiv · 2608.17406

Potential-free $L^1$-estimates for positivity-preserving Riesz transform related to Schr\"odinger operator in dimension one

Jacek Dziubański
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Abstract

Let $V\geq 0$ be a locally integrable function on $\mathbb R$. Consider the Schr\"odinger operator $L=-\frac{d^2}{dx^2} +V$. We prove that for all $0<a\leq 1$, there is a constant $C_a$, independent of $V$, such that the Riesz transform type operator $V^aL^{-a}$ is bounded on $L^1(\mathbb R)$ and $\| V^aL^{-a}f\|_{L^1(\mathbb R)}\leq C_a\|f\|_{L^1(\mathbb R)}$.

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Jacek Dziubański. 2026-08-18. Potential-free $L^1$-estimates for positivity-preserving Riesz transform related to Schr\"odinger operator in dimension one. https://arxiv.org/abs/2608.17406

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