An optimal multiplier theorem for Grushin operators in the plane, I

Gian Maria Dall'Ara, Alessio Martini

Let $\mathcal{L}=-{\partial }_x^2-V(x){\partial }_y^2$ be the Grushin operator on ${\mathbb{R}}^2$ with coefficient $V:\mathbb{R}\to [0,\infty )$. Under the sole assumptions that $V…