**Speaker:** Camillo De Lellis

Mo 15.00 - 16.45

Room: Y36M08

Th 15.00 - 16.45

Room: Y36M94

Mo 17.00 - 17.45

Y36M08

Y36M08

Übungen Harmonic Analysis

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.

Exam dates: missing

Module: MAT610 Harmonic Analysis