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arXiv · 1404.6695

Characterization of function spaces via low regularity mollifiers

Xavier Lamy·Petru Mironescu
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Abstract

Smoothness of a function $f:{\mathbb R}^n\to {\mathbb R}$ can be measured in terms of the rate of convergence of $f\astρ_\varepsilon$ to $f$, where $ρ$ is an appropriate mollifier. In the framework of fractional Sobolev spaces, we characterize the "appropriate" mollifiers. We also obtain sufficient conditions, close to being necessary, which ensure that $ρ$ is adapted to a given scale of spaces. Finally, we examine in detail the case where $ρ$ is a characteristic function.

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Xavier Lamy, Petru Mironescu. 2014-04-26. Characterization of function spaces via low regularity mollifiers. https://arxiv.org/abs/1404.6695

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