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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2015

Characterization of function spaces via low regularity mollifiers

Abstract

Smoothness of a function $f:R^n\to R$ can be measured in terms of the rate of convergence of $f\ast\rho_\epsilon$ to $f$, where $\rho$ 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 $\rho$ is adapted to a given scale of spaces. Finally, we examine in detail the case where $\rho$ is a characteristic function.
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Dates and versions

hal-00980984 , version 1 (19-04-2014)
hal-00980984 , version 2 (15-09-2014)

Identifiers

  • HAL Id : hal-00980984 , version 2

Cite

Xavier Lamy, Petru Mironescu. Characterization of function spaces via low regularity mollifiers. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (12), pp.6015-6030. ⟨hal-00980984v2⟩
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