Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials
Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 1975-2013.

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.

On montre des estimations L p pour des opérateurs de Schrödinger -Δ+V sur n et leurs racines carrées. Le potentiel est dans une classe Hölder inverse améliorant les résultats de Shen. On s’appuie sur une inégalité de type Fefferman-Phong améliorée et des inégalités Hölder inverse pour des solutions faibles de -Δ+V et leurs gradients.

DOI: 10.5802/aif.2320
Classification: 35J10, 42B20
Keywords: Schrödinger operators, maximal inequalities, Riesz transforms, Fefferman-Phong inequality, reverse Hölder estimates
Mot clés : opérateurs de Schrödinger, inégalité maximale, transformée de Riesz, inégalité de Fefferman-Phong, inégalités Hölder inverse
Auscher, Pascal 1; Ben Ali, Besma 1

1 Université de Paris-Sud, UMR du CNRS 8628 91405 Orsay Cedex (France)
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Auscher, Pascal; Ben Ali, Besma. Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schrödinger operators with nonnegative potentials. Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 1975-2013. doi : 10.5802/aif.2320. http://www.numdam.org/articles/10.5802/aif.2320/

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