8 papers
Anisotropic Bourgain--Brezis inequalities
Dmitriy Stolyarov
We provide an adjustment of the Hardy--Littlewood--Sobolev inequality for p=1 to the anisotropic setting. Several examples of anisotropic Bourgain--Brezis inequalities are obtained…
A random Lipschitz function detecting jumps
Dmitriy Stolyarov
Recently, A. Tyulenev and the author studied the class of metric spaces such that for every mapping , there exists a -Lipschitz functi…
Catching jumps of metric-valued mappings with Lipschitz functions
Dmitriy Stolyarov, Alexander Tyulenev
It follows from recent results of V. Bakhtin, R. Oleinik, and the second named author that, given a metric space , a continuous map is…
An atomic decomposition for functions of bounded variation
Daniel Spector, Cody B. Stockdale, Dmitriy Stolyarov
In this paper, we give a decomposition of the gradient measure of an arbitrary function of bounded variation into a sum of atoms , where is a set of finite p…
On the Fourier transform of measures in Besov spaces
Riju Basak, Daniel Spector, Dmitriy Stolyarov
We prove quantitative estimates for the decay of the Fourier transform of the Riesz potential of measures that are in homogeneous Besov spaces of negative exponent: \begin{align*}…
Maz'ya's -inequalities on domains
Dmitriy Stolyarov
We find necessary and sufficient conditions on the function for the inequality to be true. Here is a positive…
On dimension stable spaces of measures
Daniel Spector, Dmitriy Stolyarov
In this paper, we define spaces of measures with dimensional stability . These spaces bridge between , the space of finite Radon…
New Bellman induction and a weak version of
Egor Dobronravov, Dmitriy Stolyarov, Pavel Zatitskii
We enlarge the area of applicability of the Bellman function method to estimates in the spirit of the John--Nirenberg inequality abandoning certain convexity assumptions. As an app…