Harmonic Analysis
Programma
Interpolation of linear and sublinear operators on L^p spaces. Maximal operators and differentiation theorems. The problem of convergence of Fourier series. Elements of the theory of tempered distributions and Fourier analysis on R^n. Themes in contemporary Fourier analysis: Kakeya sets, restriction theorems etc.
Obiettivi formativi
The course is an introduction to various themes in modern Fourier analysis. Some of the methods presented in the course can be applied in many areas of analysis (and beyond), e.g., proving inequalities exploiting symmetries, the language of distributions etc.