Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces

Abstract

Let $H:=-\Delta +V$ be a nonnegative Schrödinger operator on $L^2({\mathbf{R}}^N)$, where $N\ge 2$ and $V$ is an inverse square potential. In this paper we obtain sharp decay estimates of the operator norms of $e^{-tH}$ and $\nabla e^{-tH}$ in Lorentz spaces.