Speaker: Camillo De Lellis
We start the course by studying the Fourier series and their basic
properties. Then, after introducing the set of Schwartz–class functions
and the space of tempered distributions, we study the Fourier transform.
The second part of the course is dedicated to the so called “real
variable theory”. In particular we study maximal functions, introduce
the Calderon–Zygmund decomposition, and then use it to derive properties
and estimates for singular integral operators. Finally we give an
introduction to the Littlewood–Paley theory. In the third part we
introduce the fractional integration and some spaces of weakly
differentiable functions, and we prove the Hardy–Littlewood–Sobolev
inequality together with various embedding theorems of Sobolev type.
Module: MAT610 Harmonic Analysis