Arbeitsgruppe Analysis und Partielle Differentialgleichungen


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:

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:

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