Tohoku Mathematical Journal 2000 September SECOND SERIES VOL. 52, NO. 3

 Tohoku Math. J. 52 (2000), 367-382

Title ESTIMATES OF THE FUNDAMENTAL SOLUTION FOR MAGNETIC SCHRÖDINGER OPERATORS AND THEIR APPLICATIONS

Author Kazuhiro Kurata and Satoko Sugano

(Received December 16, 1998, revised November 26, 1999)
Abstract. We study the magnetic Schrödinger operator $H$ on $\boldsymbol{R}^n$, $n\geq3$. We assume that the electrical potential $V$ and the magnetic potential $\mathbf{a}$ belong to a certain reverse Hölder class, including the case that $V$ is a non-negative polynomial and the components of $\mathbf{a}$ 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.

1991 Mathematics Subject Classification. Primary 42B20; Secondary 35J10, 35B45.

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