We prove the $L^p$-differentiability at almost every point for convolution products on $R^d$ of the form $K*\mu$, where $\mu$ is bounded measure and $K$ is a homogeneous kernel of degree $1-d$. From this result we derive the $L^p$-differentiability for vector fields on $R^d$ whose curl and divergence are measures, and also for vector fields with bounded deformation.

### On the L^p-differentiability of certain classes of functions

#### Abstract

We prove the $L^p$-differentiability at almost every point for convolution products on $R^d$ of the form $K*\mu$, where $\mu$ is bounded measure and $K$ is a homogeneous kernel of degree $1-d$. From this result we derive the $L^p$-differentiability for vector fields on $R^d$ whose curl and divergence are measures, and also for vector fields with bounded deformation.
##### Scheda breve Scheda completa Scheda completa (DC)
Alberti, Giovanni; Stefano, Bianchini; Gianluca, Crippa
File in questo prodotto:
File
abc-differentiability-v1.5.pdf

accesso aperto

Descrizione: articolo (versione finale inviata all'editore)
Tipologia: Documento in Post-print
Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/245399