On bilinear estimates for wave equations

I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of " Bilinear Estimates" . In addition to the L2 theory, which is now quite well developed, I plan to discuss a more general point of view concerning the U theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also plan to discuss the relevance of these estimates to nonlinear wave equations.