# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Square functions associated to Schrödinger operators

### Tom 203 / 2011

Studia Mathematica 203 (2011), 171-194 MSC: Primary 35J10, 42B35; Secondary 46B20, 42B25. DOI: 10.4064/sm203-2-4

#### Streszczenie

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.

#### Autorzy

• I. Abu-FalahahDepartamento de Matemáticas
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• P. R. StingaDepartamento de Matemáticas
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• J. L. TorreaDepartamento de Matemáticas