# Multilinear wave estimates

### Multilinear estimates

There are some isolated examples of multilinear estimates that cannot be obtained from linear and bilinear estimates and Holder's inequality. For instance, the inequality

${\displaystyle |\int D^{-a}D_{-}(u_{1}u_{2})u_{3}u_{4}dxdt|<~||f_{1}||_{H^{n/2-a}}||f_{2}||_{2}||f_{3}||_{2}||f_{4}||_{2}}$

is proven for ${\displaystyle d=2}$ and ${\displaystyle 3/4 in Sb-p.