Lehrinhalte
Fourier transform and tempered distributions
Singular integral operators of convolution type
Real Hardy spaces
Bounded mean oscillation
(Non-tangential) maximal functions and Carleson measures
Singular integrals of non-convolution type and the T(1) Theorem
Quadratic estimates and applications
Literature
E.M. Stein, Harmonic Analysis, Princeton Mathematical Series, 1993.
L. Grafakos, Modern Fourier Analysis, Springer, 2009.
Voraussetzungen
Measure theory and integration
Basic knowledge of Sobolev spaces and distributions
Official Course Description
My lecture will be an introduction to (some) foundations of modern harmonic analysis. We will see proofs of some challening questions in the field during the last decades and end with problems from current research.
Fourier transform and tempered distributions
Singular integral operators of convolution type
Real Hardy spaces
Bounded mean oscillation
(Non-tangential) maximal functions and Carleson measures
Singular integrals of non-convolution type and the T(1) Theorem
Quadratic estimates and applications
Literature
E.M. Stein, Harmonic Analysis, Princeton Mathematical Series, 1993.
L. Grafakos, Modern Fourier Analysis, Springer, 2009.
Voraussetzungen
Measure theory and integration
Basic knowledge of Sobolev spaces and distributions
Official Course Description
My lecture will be an introduction to (some) foundations of modern harmonic analysis. We will see proofs of some challening questions in the field during the last decades and end with problems from current research.
- Lehrende: Tim Böhnlein
- Lehrende: Moritz Egert
- Lehrende: Benjamin Wolfgang Kosmala
Semester: ST 2022