Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

V4B5 - Real and harmonic analysis (Winter term 2014/2015)

Lecturer:

Prof. Dr. Herbert Koch

TA:

Gennady Uraltsev

Lectures

• Mo 14.15-16.00, room 1.008
• We 8.15-10.00, room 1.008

TA groups:

• Fr 16:00-18:00, room 1.007

Exercise Sheets:

• 08.10 - 15.10
• 15.10 - 22.10
• 22.10 - 29.10
• 29.10 - 05.11
• 05.11 - 12.11
• 12.11 - 19.11
• 19.11 - 26.11
• 26.11 - 3.12
• 10.12 - 17.12
• 07.01 - 14.01
• 14.01 - 21.01
• 21.01 - 28.01

Contents:

The course introduces the key concepts of real and harmonic analysis, a number of important expamples, and their relation to partial differential equations. Keywords are: Fourier series: Convergence and examples, boundary values of harmonic functions, Maximal function, square functions and singular integrals, Lebesgue spaces, Hardy space, BMO and Littlewood-Paley theory, almost orthogonality, uncertainty and Fourier restriction. Application to PDE.

Notes:

• until 04.02.2015

Oral examination

• February 19-20, 2015
• March 30-31, 2015

Literature:

• Muscalu and Schlag: Classical and multilinear harmonic analysis, Vol 1, Cambridge studies in advanced mathematics 137, 2013
• Grafakos: Classical Fourier Analysis, Springer, Graduate Texts in Mathematics 249, 2008