Slow points for functions in the Zygmund class Λd*.

Abstract

Using probabilistic methods, we find the exact Hausdorff measure function and dimension of sets of dyadic Lipschitz points (i.e., slow points) for functions belonging to particular Zygmund-type classes. We then explore, in depth, the relationship between sets of slow points and sets of standard Lipschitz points, both in the particular case of the van der Waerden--Takagi function and for more general dyadic Zygmund functions.