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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 of an arbitrary function of bounded variation into a sum of atoms , where 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.FA2025
An atomic decomposition of one-dimensional metric currents without boundary
You-Wei Benson Chen, Jesse Goodman, Felipe Hernandez +1
This paper proves an atomic decomposition of the space of -dimensional metric currents without boundary, in which the atoms are specified by closed Lipschitz curves with uniform…