Square functions associated to Schrödinger operators
Volume 203 / 2011
Studia Mathematica 203 (2011), 171-194
MSC: Primary 35J10, 42B35; Secondary 46B20, 42B25.
DOI: 10.4064/sm203-2-4
Abstract
We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrödinger operators of the form $\mathcal L=-{\mit\Delta}+V$, where the nonnegative potential $V$ satisfies a reverse Hölder inequality. The main idea is to sharpen the well known localization method introduced by Z. Shen. Our results can be regarded as alternative proofs of the boundedness in $H^1$, $L^p$ and BMO of classical $\mathcal L$-square functions.
