ABSTRACT
The purpose of this chapter is to present some of the most important theorems on Fourier analysis in ℝ n . These theorems are the Marcinkiewicz interpolation theorem, the Calderon Zygmund decomposition, Mihlin’s theorem, and the Calderon Zygmund theory of singular integrals. They are all fundamental results whose proofs depend on the methods of real analysis. Our purpose is to present proofs of these theorems, showing how they follow from these methods. We leave their application to other works.
