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

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

2006-05-02

arxiv.org/abs/math/0605047v3

Mathematics

Analysis of PDEs

Revised version

Scientific paper

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

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