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

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

is proven for $d=2$ and $3/4<a<1$ in Sb-p.