LEARNING OUTCOMES
* using dyadic cubes as a tool for problems in mathematical analysis
* estimating transformations of functions in different norms both “from scratch” and by interpolating and extrapolating previously available results
* rigorous reasoning with singular integrals
Credits: 5
Schedule: 21.10.2024 - 11.12.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Tuomas Hytönen
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Dyadic cubes
Calderon-Zygmund decomposition
Functions of bounded mean oscillation
Muckenhoupt weights
Singular integrals
Interpolation and extrapolation of operator norm inequalities
Note: Harmonic analysis was historically understood as a synonym to Fourier analysis, but in the modern usage, harmonic analysis is seen as a broader term. Since Fourier analysis is covered in other courses, this course emphasizes aspects of harmonic analysis other than those related to Fourier series/transform.
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: lectures, exercises and exam.
Assessment methods: exercises and an exam.
Workload
valid for whole curriculum period:
contact hours 36h (no compulsory attendance)
self-study ca 100h
DETAILS
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Autumn II
2025-2026 No teaching