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

Auscher, Pascal; Ben Ali, Besma

Maximal inequalities and Riesz transform estimates on

L^{p}

spaces for Schrödinger operators with nonnegative potentials
[Inégalité maximale et de transformée de Riesz dans

L^{p}

pour des opérateurs de Schrödinger avec potentiels positifs]

Auscher, Pascal ; Ben Ali, Besma

Annales de l'Institut Fourier, Tome 57 (2007), p. 1975-2013 / Harvested from Numdam

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Résumé
Abstract

On montre des estimations $L^{p}$ pour des opérateurs de Schrödinger $- Δ + V$ sur $ℝ^{n}$ 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.

We show various $L^{p}$ estimates for Schrödinger operators $- Δ + V$ on $ℝ^{n}$ 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 $- Δ + V$ and their gradients.

Publié le : 2007-01-01

MR 2377893 | Zbl 1161.35003

DOI : https://doi.org/10.5802/aif.2320
Classification: 35J10, 42B20
Mots clés: opérateurs de Schrödinger, inégalité maximale, transformée de Riesz, inégalité de Fefferman-Phong, inégalités Hölder inverse

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     author = {Auscher, Pascal and Ben Ali, Besma},
     title = {Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schr\"odinger operators with nonnegative potentials},
     journal = {Annales de l'Institut Fourier},
     volume = {57},
     year = {2007},
     pages = {1975-2013},
     doi = {10.5802/aif.2320},
     zbl = {1161.35003},
     mrnumber = {2377893},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2007__57_6_1975_0}
}

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, Tome 57 (2007) pp. 1975-2013. doi : 10.5802/aif.2320. http://gdmltest.u-ga.fr/item/AIF_2007__57_6_1975_0/

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