Harmonic Analysis on Euclidean Spaces

The course presents some of the main topics in Euclidean Harmonic Analysis. It consists of three parts:

1. Inequalities and linear operators in Lp spaces, where we discuss techniques (symmetries, duality, interpolation, the "tensor power trick", dimensional analysis) useful to establish various functional inequalities.

2. Fourier Analysis, where we discuss the Fourier transform in various degrees of generality: L1 theory, L2 theory, distributional theory.

3. Calderón-Zygmund theory, where we study singular integrals, maximal operators, quadratic functions and their applications to various problems in analysis.