On Kato-Ponce and fractional Leibniz

Dong Li

We show that in the Kato-Ponce inequality $\Vert J^s(fg)-f{J}^{s}g{\Vert }_p\lesssim \Vert \partial f{\Vert }_{\infty }\Vert J^{s-1}g{\Vert }_p+\Vert J^{s}f{\Vert }_p\Vert g{\Vert }_{\infty }$, the $J^{s}f$ term on the RHS ca…