Tohoku Mathematical Journal

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

Kazuhiro Kurata and Satoko Sugano

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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

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

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J10: Schrödinger operator [See also 35Pxx]
Secondary: 35E05: Fundamental solutions


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.

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