L p estimates for Schrödinger operators with certain potentials
Annales de l'Institut Fourier, Volume 45 (1995) no. 2, p. 513-546

We consider the Schrödinger operators -Δ+V(x) in n where the nonnegative potential V(x) belongs to the reverse Hölder class B q for some qn/2. We obtain the optimal L p estimates for the operators (-Δ+V) iγ , 2 (-Δ+V) -1 ,(-Δ+V) -1/2 and (-Δ+V) -1 where γ. In particular we show that (-Δ+V) iγ is a Calderón-Zygmund operator if VB n/2 and (-Δ+V) -1/2 ,(-Δ+V) -1 are Calderón-Zygmund operators if VB n .

Nous considérons des opérateurs de Schrödinger -Δ+V(x) dans n où le facteur non négatif V(x) appartient à la classe de Hölder inversée B q pour tout qn/2. Nous obtenons les estimations optimales L p pour les opérateurs (-Δ+V) iγ , 2 (-Δ+V) -1 ,(-Δ+V) -1/2 et (-Δ+V) -1 γ. En particulier nous montrons que (-Δ+V) iγ est un opérateur de Calderón-Zygmund si VB n/2 and (-Δ+V) -1/2 ,(-Δ+V) -1 sont des opérateurs de Calderón-Zygmund si VB n .

@article{AIF_1995__45_2_513_0,
     author = {Shen, Zhongwei},
     title = {$L^p$ estimates for Schr\"odinger operators with certain potentials},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {2},
     year = {1995},
     pages = {513-546},
     doi = {10.5802/aif.1463},
     zbl = {0818.35021},
     mrnumber = {96h:35037},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1995__45_2_513_0}
}
Shen, Zhongwei. $L^p$ estimates for Schrödinger operators with certain potentials. Annales de l'Institut Fourier, Volume 45 (1995) no. 2, pp. 513-546. doi : 10.5802/aif.1463. http://www.numdam.org/item/AIF_1995__45_2_513_0/

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