1Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain 2Departamento 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
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.
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
Affiliations des auteurs :
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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author = {I. Abu-Falahah and P. R. Stinga and J. L. Torrea},
title = {Square functions associated to {Schr\"odinger} operators},
journal = {Studia Mathematica},
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AU - P. R. Stinga
AU - J. L. Torrea
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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
