11 citations · 13 across the 5 of their papers we have counts for
7 papers
Alberti's type rank one theorem for martingales
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the -regular filtration. This dep…
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 finite configurations in the spectra of singular measures
Rami Ayoush
We establish various forms of the following certainty principle: a set contains a given finite linear pattern, provided that is a support of the Four…
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…
On dimension and regularity of bundle measures
Rami Ayoush, Michał Wojciechowski
In this paper we quantify the notion of antisymmetry of the Fourier transform of certain vector valued measures. The introduced scale is related to the condition appearing in Uchiy…