Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher[1]; Besma Ben Ali[1]

  • [1] Université de Paris-Sud, UMR du CNRS 8628 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 6, page 1975-2013
  • ISSN: 0373-0956

Abstract

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We show various L p estimates for Schrödinger operators - Δ + V on n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of - Δ + V and their gradients.

How to cite

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Auscher, Pascal, and Ben Ali, Besma. "Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials." Annales de l’institut Fourier 57.6 (2007): 1975-2013. <http://eudml.org/doc/10284>.

@article{Auscher2007,
abstract = {We show various $L^p$ estimates for Schrödinger operators $-\Delta +V$ on $\mathbb\{R\}^n$ and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of $-\Delta +V$ and their gradients.},
affiliation = {Université de Paris-Sud, UMR du CNRS 8628 91405 Orsay Cedex (France); Université de Paris-Sud, UMR du CNRS 8628 91405 Orsay Cedex (France)},
author = {Auscher, Pascal, Ben Ali, Besma},
journal = {Annales de l’institut Fourier},
keywords = {Schrödinger operators; maximal inequalities; Riesz transforms; Fefferman-Phong inequality; reverse Hölder estimates; Riesz transforms, Fefferman-Phong inequality},
language = {eng},
number = {6},
pages = {1975-2013},
publisher = {Association des Annales de l’institut Fourier},
title = {Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials},
url = {http://eudml.org/doc/10284},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Auscher, Pascal
AU - Ben Ali, Besma
TI - Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 6
SP - 1975
EP - 2013
AB - We show various $L^p$ estimates for Schrödinger operators $-\Delta +V$ on $\mathbb{R}^n$ and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of $-\Delta +V$ and their gradients.
LA - eng
KW - Schrödinger operators; maximal inequalities; Riesz transforms; Fefferman-Phong inequality; reverse Hölder estimates; Riesz transforms, Fefferman-Phong inequality
UR - http://eudml.org/doc/10284
ER -

References

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