We study the L^∞(Rᵈ) boundedness for Riesz transforms of the form Vᵃ(-12Δ+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).
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Maciej Kucharski (2024) studied this question.
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