Abstract：

In this talk, we discuss the $W^{s,p}$-boundedness for stationary wave operators of the Schr\"odinger operator with inverse-square potential $$\mathcal L_a=-\Delta+\tfrac{a}{|x|^2}, \quad a\geq  -\tfrac{(d-2)^2}{4}, \quad d\geq 2. $$ We will explain how to construct the stationary wave operators in terms of integrals of Bessel functions and  spherical harmonics, and  prove that they are $W^{s,p}$-bounded for certain $p$ and $s$ which depend on $a$. As corollaries,  we  prove  dispersive estimates and generalize some known results such as the  uniform Sobolev inequalities, the equivalence of Sobolev norms to a larger range of indices. This  talk is based on a joint work with Changxing Miao and Jiqiang Zheng. 

Bio：

Dr. Xiaoyan Su is currently a postdoc at Beijing Normal University who graduated from Sichuan University. She is interested in the spectral theory and dispersive PDEs.