Dimension-free estimates for positivity-preserving Riesz transforms related to Schrödinger operators with certain potentials

We study the $L^{\mathrm{\infty }}({\mathbb{R}}^d)$ boundedness for Riesz transforms of the form $V^a(-\frac{1}{2}\mathrm{\Delta }+V{)}^{-a},$ 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 $a⩽1$ are obtained on $L^1({\mathbb{R}}^d)$.