Research Interests

My research interests lie in the areas of harmonic analysis, functional analysis, analysis on metric measure spaces, and partial differential equations. 

Very often, my work focusses on different function spaces. Some of my interests:

• the behaviour (boundedness, continuity) of non-linear operators (rearrangements, maximal functions) on various function spaces that are defined in terms of mean oscillation (BMO, VMO, JN_p) in both the Euclidean setting and the setting of metric measure spaces;

• nonlinear potential theory (boundary-value problems) on domains in metric measure spaces, especially unbounded ones;

• Schroedinger operators (spectral approximation, unique continuation).

Some areas in which I do not yet have any work but have interest in: convex analysis, geometric measure theory, optimal transport, geometric probability, Bellman function techniques, Calderón-Zygmund singular integral operators, analytic function spaces.