Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows

We consider a Schr\"odinger hamiltonian $H$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positively definite. We prove the following: if $\|e^{-itH}\|_{L^1\to L^\infty}\leq Ct^{-n/2}$, then $ \||x|^{-g(n)}e^{-itH}|x|^{-g(n)}\|_{L^1\to L^\infty}\leq Ct^{-n/2-g(n)}$, being $g(n)$ a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$.