Characterization of function spaces via low regularity mollifiers

Xavier Lamy (1) , Petru Mironescu (2)

1 EDPA - Équations aux dérivées partielles, analyse
2 ICJ - Institut Camille Jordan

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.

Mots clés: Besov spaces; approximation by smoothing

Domaines: Analyse fonctionnelle [math.FA]

Xavier Lamy, Petru Mironescu. Characterization of function spaces via low regularity mollifiers. 2014. ⟨hal-00980984v1⟩