$L^p$ boundedness of pseudo-differential operators with symbols in $S_{\rho ,1}^{n(\rho -1)/2}$

Jingwei Guo, Xiangrong Zhu

For symbol $a\in S_{\rho ,1}^{n(\rho -1)/2}$ the pseudo-differential operator $T_a$ may not be $L^2$ bounded. However, under some mild extra assumptions on $a$, we show that $T_a$ is bound…