- Maximal regularity of elliptic operators
- Sectorial operators and their regularity properties
- Semigroup theory
- Functional calculi
- Harmonic analysis on Banach spaces
Lecture notes of previous courses:
During my time as a doctoral and postdoctoral studies my research was focused on the maximal L^p-regularity of abstract Cauchy problems and related issues, such as the holomorphic functional calculus for sectorial operators. During my PhD I was mainly interested in structural questions. In particular, I studied the extrapolation problem for maximal regularity. As a postdoc my focus lied on the maximal regularity of non-autonomous elliptic operators. Moreover, I have done some research on harmonic analysis on Banach spaces (operator-valued Fourier multipliers and Calderón-Zygmund operators).
Further, I am interested in the theory of one parameter semigroups (C_0-semigroups) and in the geometry of Banach spaces, particularly in view of possible applications to semigroup theory.