Characterization of function spaces via low regularity mollifiers
Résumé
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.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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