The $L^p$-boundedness of wave operators for 4-th order Schrödinger operators on $\mathbb{R}^2$, I

Abstract: We prove that high energy parts of wave operators for fourth order Schr\"odinger operators $H=\Delta^2 + V(x)$ in $\mathbb{R}^2$ are bounded in $L^p(\mathbb{R}^2)$ for $p\in(1,\infty)$.