Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups

Abstract

Let $H:=-\Delta +V$ be a nonnegative Schrödinger operator on $L^2({\mathbf{R}}^N)$, 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 $t\to \infty$.

Cited by in corpus (2)

• Anisotropic Hardy-Lorentz Spaces and Their Applications
• Large time behavior of solutions of the heat equation with inverse square potential