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

Auscher, Pascal; Ben Ali, Besma

Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 1975-2013.

On montre des estimations $L^p$ pour des opérateurs de Schrödinger $-\Delta +V$ 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 $-\Delta +V$ et leurs gradients.

We show various $L^p$ estimates for Schrödinger operators $-\Delta +V$ 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 $-\Delta +V$ and their gradients.

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

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