## Tohoku Mathematical Journal

### Estimates of the fundamental solution for magnetic Schrödinger operators and their applications

#### Abstract

We study the magnetic Schrödinger operator $H$ on $R^n$, $n\geq3$. We assume that the electrical potential $V$ and the magnetic potential {\bf a} belong to a certain reverse Hölder class, including the case that $V$ is a non-negative polynomial and the components of {\bf a} are polynomials. We show some estimates for operators of Schrödinger type by using estimates of the fundamental solution for $H$. In particular, we show that the operator $\nabla^2(-\Delta+V)^{-1}$ is a Calderón-Zygmund operator.

#### Article information

Source
Tohoku Math. J. (2), Volume 52, Number 3 (2000), 367-382.

Dates
First available in Project Euclid: 3 May 2007

https://projecteuclid.org/euclid.tmj/1178207819

Digital Object Identifier
doi:10.2748/tmj/1178207819

Mathematical Reviews number (MathSciNet)
MR1772803

Zentralblatt MATH identifier
0967.35035

Subjects
Secondary: 35E05: Fundamental solutions

#### Citation

Kurata, Kazuhiro; Sugano, Satoko. Estimates of the fundamental solution for magnetic Schrödinger operators and their applications. Tohoku Math. J. (2) 52 (2000), no. 3, 367--382. doi:10.2748/tmj/1178207819. https://projecteuclid.org/euclid.tmj/1178207819

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