Harmonic Analysis

This course gives an introduction into real harmonic analysis. Harmonic analysis has its origin in Fourier's work on the heat equation. Nowadays, it provides important tools in tackling a large variety of problems coming from elliptic and parabolic partial differential equation, in particular in boundary value problems. The theory has close links with operator theory and spectral theory.

In this course, we will develop important concepts of real harmonic analysis, including:

- covering lemmas and maximal functions

- basic interpolation theory

- Hilbert transform, Riesz transform and Cauchy transform

- Calderón-Zygmund operators (singular integral operators)

- Mikhlin multiplier theorem

- Littlewood-Paley theory