Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition

We consider the fifth order KdV type equations and prove the unconditional well-posedness in $H^s(\mathbb{T})$ for $s \ge 1$. It is optimal in the sense that the nonlinear terms can not be defined in the space-time distribution framework for $s<1$. The main idea is to employ the normal form reduction and a kinds of cancellation properties to deal with the derivative losses.