Sharp $L^p$ estimates for Schrödinger groups on spaces of homogeneous type

The Anh Bui, Piero D'Ancona, Fabio Nicola

We prove an $L^p$ estimate $$\Vert e^{-itL}\phi (L)f{\Vert }_p\lesssim (1+|t|{)}^s\Vert f{\Vert }_p,t\in \mathbb{R},s=n\left|\frac{1}{2}-\frac{1}{p}\right|$$ for the Schrödinger group…