The decay rate of Hormander lemma is optimal or not?

Question

The Hormander lemma about oscillatory integral operators states that $T_\lambda f(x)=\int e^{i\lambda S(x,y)}a(x,y)f(y)dy$, while the Hessian of $S(x,y)$ is nondegenerate, then $||T_\lambda||_2 \leq C\lambda^{-n/2}$. I wonder if this decay rate is optimal in the sense that for every $S(x,y)$ satisfying the non-degenerate condition, we can choose appropriate $a(x,y)$ and $f(y)(||f||_2 =1)$ such that $||T_\lambda f||_2 \geq C^{*}λ^{−n/2}$?