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