V4B5 - Real and Harmonic Analysis
Summer term 2025
Organisational details
- Time and place: Mo. and Th. 14-16 (c.t.) Room 0.006, Endenicher Allee 60, first lecture: Mo April 14th
- Exercises: Tu 10-12 and Th 16-18 (c.t.) Room 1.008, Endenicher Allee 60, first exercise: Tu April 15th
-
See the syllabus for further details.
- If you are a participating Masters student, please register on Basis.
Overview
In this course, we will cover several classical topics, including the Hardy Littlewood maximal function, Calderon-Zygmund theory, Singular integrals, stationary phase, multiplier theory, Littlewood-Paley theory and pointwise convergence of Fourier series. If time permits, we will cover additional topics, which may include time frequency analysis and weighted norm inequalities.
Prerequisites: Basic Bachelor level courses in Analysis. In particular familiarity with Fourier analysis and Lebesgue measure theory is helpful.
Homework: There will be weekly homework assignments and tutorials. Students will have to obtain half of the available homework points to be admitted to the exam.
Course text: Our main text of reference will be "Classical and Multilinear Harmonic Analysis" by Muscalu-Schlag. We will however supplement with other resources, such as "Classical Fourier Analysis" by Grafakos, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" by Stein, and other resources. We will also lean on some research papers for the additional topics.