Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Let $H:=-Δ+V$ be a nonnegative Schrödinger operator on $L^2({\bf R}^N)$, where $N\ge 2$ and $V$ is a radially symmetric function decaying quadratically at the space infinity. In this paper we consider the Schrödinger heat semigroup $e^{-tH}$, and make a complete table of the decay rates of the operator norms of $e^{-tH}$ in the Lorentz spaces as $t\to\infty$.

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