Square functions associated to Schrodinger operators

Details Square functions associated to Schrodinger operators Square functions associated to Schrodinger operators

2010-09-28

arxiv.org/abs/1009.5569v2

Mathematics

Classical Analysis and ODEs

17 pages, revised version following referee's comments, to appear in Studia Mathematica

Scientific paper

We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrodinger operators of the form $L=-\Delta+V$, where the nonnegative potential $V$ satisfies a reverse Holder 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 $L$-square functions.

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