8 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…
On the Embedding of Space into Besov-Orlicz Space
Aleksander Pawlewicz, Michał Wojciechowski
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces…
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…
An invariant variant of the little Grothendieck theorem for Sobolev spaces
Krystian Kazaniecki, Piotr Pakosz, Michał Wojciechowski
We prove that every Hilbert space operator which factorizes invariantly through Sobolev space belongs to some non-trivial Schatten class.
Hoeffding decomposition in spaces
Maciej Rzeszut, Michał Wojciechowski
The well known result of Bourgain and Kwapień states that the projection onto the subspace of the Hilbert space spanned by functions depende…