## Tokyo Journal of Mathematics

### $L^p$ Estimates for Some Schrödinger Type Operators and a Calderóon-Zygmund Operator of Schrödinger Type

Satoko SUGANO

#### Abstract

We consider the Schrödinger and Schrödinger type operators $H_{1}=-\Delta+V$ and $H_2=(-\Delta)^2+V^2$ with non-negative potentials $V$ on $\mathbf{R}^n$. We assume that the potential $V$ belongs to the reverse Hölder class which includes non-negative polynomials. We establish estimates of the fundamental solution for $H_{2}$ and show some $L^p$ estimates for Schrödinger type operators. Moreover, we show that the operator $\nabla^4H_{2}^{-1}$ is a Calderón-Zygmund operator.

#### Article information

Source
Tokyo J. Math., Volume 30, Number 1 (2007), 179-197.

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.tjm/1184963655

Digital Object Identifier
doi:10.3836/tjm/1184963655

Mathematical Reviews number (MathSciNet)
MR2328062

Zentralblatt MATH identifier
1207.35112

#### Citation

SUGANO, Satoko. $L^p$ Estimates for Some Schrödinger Type Operators and a Calderóon-Zygmund Operator of Schrödinger Type. Tokyo J. Math. 30 (2007), no. 1, 179--197. doi:10.3836/tjm/1184963655. https://projecteuclid.org/euclid.tjm/1184963655

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