# Hipoelliptic altered wave operator?

We know that the wave operator in $$\mathbb{R}^{2}$$:

$$L=\frac{\partial^2}{\partial x^2}-\frac{\partial^2}{\partial y^2}$$

Can I say that $$L-\lambda$$, $$\lambda(x,y) \in C^\infty(\mathbb{R}^2)$$ is not hypoelliptic?

I tried use $$\lambda$$ with rapidly decay (to apply the Fourier transform and find an fundamental solution) to find $$\lambda$$ such that $$L-\lambda$$ is hipoelliptic, but it isn't so easy.