Dmitriy Stolyarov

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20242026

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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 $μ = D χ_{F}$ , where $F$ is a set of finite p…

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*}…

math.FA2024

On dimension stable spaces of measures

Daniel Spector, Dmitriy Stolyarov

In this paper, we define spaces of measures $D S_{β} (R^{d})$ with dimensional stability $β \in (0, d)$ . These spaces bridge between $M_{b} (R^{d})$ , the space of finite Radon…