El Maati Ouhabaz
Published 2017-05-18Version 1
We study boundedness on $L^p(R^d)$ of vertical Littlewood-Paley-Stein functions for Schr\"odinger operators $-\Delta + V$ with nonnegative potential $V$. These functions are proved to be bounded on $L^p$ for all $p \in (1, 2]$. The situation for $p > 2$ is different. We prove for a class of potentials that the boundedness on $L^p$ for some $p > d$ holds if and only if $V= 0$.
A Liouville-type theorem for Schrödinger operators
Schrödinger Operators With $A_\infty$ Potentials
Propagation for Schrödinger operators with potentials singular along a hypersurface
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