Microlocal approach to the Hausdorff dimension of measures

During the talk I will discuss the proof of a generalization of the Aleksandrov-Forelli theorem about regularity of pluriharmonic measures. This result is established via modification of the method of microlocalizing spectral properties of measures due to R.G.M. Brummelhuis: in our case the properties of the so-called s-Riesz sets are expressed in terms of the wave front set.
This is joint work with Michael Wojciechowski.