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Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher·Besma Ben Ali
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Abstract

We show various $L^p$ estimates for Schrödinger operators $-Δ+V$ on $\RR^n$ and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen \cite{Sh1}. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of $-Δ+V$ and their gradients.

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Pascal Auscher, Besma Ben Ali. 2007-02-10. Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials. https://arxiv.org/abs/math/0605047

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