Geodesic
Square functions associated to Schrödinger operators
I. Abu-Falahah1 ; P. R. Stinga1 ; J. L. Torrea2
1 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
2 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid and ICMAT-CSIC-UAM-UCM-UC3M 28049 Madrid, Spain
Studia Mathematica, Tome 203 (2011) no. 2, pp. 171-194 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm203-2-4
Keywords: characterize geometric properties banach spaces terms boundedness square functions associated general schr dinger operators form mathcal mit delta where nonnegative potential satisfies reverse lder inequality main idea sharpen known localization method introduced shen results regarded alternative proofs boundedness bmo classical mathcal l square functions

I. Abu-Falahah 1 ; P. R. Stinga 1 ; J. L. Torrea 2

1 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
2 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid and ICMAT-CSIC-UAM-UCM-UC3M 28049 Madrid, Spain 
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     title = {Square functions associated to {Schr\"odinger} operators},
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I. Abu-Falahah; P. R. Stinga; J. L. Torrea. Square functions associated to Schrödinger operators. Studia Mathematica, Tome 203 (2011) no. 2, pp. 171-194. doi: 10.4064/sm203-2-4

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