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Zbl 0818.35021
Shen, Zhongwei
$L\sp p$ estimates for Schrödinger operators with certain potentials. (English)
[J] Ann. Inst. Fourier 45, No.2, 513-546 (1995). ISSN 0373-0956; ISSN 1777-5310/e

Summary: We consider the Schrödinger operators $-\Delta +V(x)$ in ${\bbfR}\sp n$ where the nonnegative potential $V(x)$ belongs to the reverse Hölder class $B\sb q$ for some $q\geq n\slash 2$. We obtain the optimal $L\sp p$ estimates for the operators $(- \Delta +V)\sp{i\gamma},\nabla\sp 2 (- \Delta +V)\sp{-1}, \nabla (- \Delta +V)\sp{-1\slash 2}$ and $\nabla(- \Delta +V)\sp{-1}$ where $\gamma\in{\bbfR}$. In particular we show that $(- \Delta +V)\sp{i\gamma}$ is a Calderón-Zygmund operator if $V\in B\sb{n\slash 2}$ and $\nabla (- \Delta +V)\sp{-1\slash 2}, \nabla (- \Delta +V)\sp{-1}\nabla$ are Calderón-Zygmund operators if $V\in B\sb n$.

MSC 2000:: *35J10 Schroedinger operator
42B20 Singular integrals, several variables

Keywords: $L\sp p$ estimates; reverse Hölder class

Cited in: Zbl 1251.22007 Zbl 1203.42029 Zbl 1161.35003 Zbl 0929.22005

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