# Applications of the Calderon-Zygmund theory to PDE's

I am planning to build a PDE topics course focussing on the Calderon-Zygmund theory. I know some important applications of the Calderon-Zygmund theory to elliptic PDEs, but I don't know enough to get the whole picture (I have an impression that it is used in hyperbolic problems also). My question is, what are my choices on the "applications" part of the course? One application per answer, and please include references if possible.

To get started, I have the following examples (please expand these if you want)

• Standard elliptic estimates for the Laplacian in the $L^p$ setting can be established by using the Calderon-Zygmund theory applied to the Riesz potential.

• Elliptic estimates for more general constant coefficient operators can be proved by using the Littlewood-Paley theory, which in turn is established by using the Calderon-Zygmund type estimates.