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.