Uniform $L^2$-bounds for the $n$-th Calderón commutator on Lipschitz graphs

Joan Hernández, Joan Mateu, Laura Prat

We prove that, for every real Lipschitz function $A$ and every integer $n\ge 1$, $\Vert T_{A,n}{\Vert }_{L^2(\mathbb{R})\to L^2(\mathbb{R})}\le C\Vert A^{\prime }{\Vert }_{\infty }^n$, where $T_{A,n}$ is the $n$…