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On L p estimates for positivity-preserving Riesz transforms related to Schrödinger operators

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Boundedness of Riesz transforms of the form Va(−1/2Δ+V) is established when conditions on potential V are met.
For 1<p≤2, it is proven that Va(−1/2Δ+V) remains bounded in l p(ℝd), emphasizing the integral condition on V.
This work extends findings to show l ∞ and l 1 boundedness for non-negative potentials with specific growth types.
Counterexamples indicate failures in boundedness under certain conditions, underscoring the robustness of potential assumptions.

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This analysis demonstrates boundedness for Riesz transforms in l p spaces, indicating conditions on potentials.

Kucharski et al. (2025) studied this question.

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