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, p. 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 : https://doi.org/10.5802/aif.2320
Classification:  35J10,  42B20
Keywords: Schrödinger operators, maximal inequalities, Riesz transforms, Fefferman-Phong inequality, reverse Hölder estimates
@article{AIF_2007__57_6_1975_0,
     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     pages = {1975-2013},
     doi = {10.5802/aif.2320},
     zbl = {1161.35003},
     mrnumber = {2377893},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_6_1975_0}
}
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. https://aif.centre-mersenne.org/item/AIF_2007__57_6_1975_0/

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