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

Let $H:=-Δ+V$ be a nonnegative Schrödinger operator on $L^2({\bf R}^N)$, 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.

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