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

We study the L^ (Rᵈ) boundedness for Riesz transforms of the form V^{a (-12+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 L¹ (Rᵈ).