Square functions associated to Schrödinger operators

Tom 203 / 2011

I. Abu-Falahah, P. R. Stinga, J. L. Torrea 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
    Facultad de Ciencias
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail
  • P. R. StingaDepartamento de Matemáticas
    Facultad de Ciencias
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail
  • J. L. TorreaDepartamento de Matemáticas
    Facultad de Ciencias
    Universidad Autónoma de Madrid
    and
    ICMAT-CSIC-UAM-UCM-UC3M
    28049 Madrid, Spain
    e-mail

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