Dmitriy Stolyarov

collaborators

5 papers

math.CA2026

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…

math.MG2026

A random Lipschitz function detecting jumps

Dmitriy Stolyarov

Recently, A. Tyulenev and the author studied the class of metric spaces $X$ such that for every mapping $γ : [0, 1] \to X$ , there exists a $1$ -Lipschitz functi…

math.CA2026

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 $X$ , a continuous map $I^^{3} : [a, b] \to X$ is…

math.FA2025

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 $D u$ of an arbitrary function of bounded variation $u$ into a sum of atoms $I^¼ = D I ¨ _{F}$ , where $F$ is a set of finite…

math.FA2025

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*}…