4 papers
Dimensional estimates for measures on quaternionic spheres
Rami Ayoush, Michał Wojciechowski
In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This…
Microlocal approach to the Hausdorff dimension of measures
Rami Ayoush, Michał Wojciechowski
In this paper we study the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. This is achi…
Hausdorff dimension of measures with arithmetically restricted spectrum
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via app…
Martingale approach to Sobolev embedding theorems
Rami Ayoush, Dmitriy Stolyarov, Michal Wojciechowski
We prove a martingale analog of van Schaftingen's theorem and give sharp estimates on the lower Hausdorff dimension of measures in martingale shift invariant spaces. We also provid…