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arXiv · 1705.06794

Littlewood-Paley-Stein functions for Schrödinger operators

El Maati Ouhabaz
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Abstract

We study boundedness on $L^p(R^d)$ of vertical Littlewood-Paley-Stein functions for Schrödinger operators $-Δ+ V$ 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 $V= 0$.

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El Maati Ouhabaz. 2017-05-18. Littlewood-Paley-Stein functions for Schrödinger operators. https://arxiv.org/abs/1705.06794

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