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.
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Alberti, Giovanni; Stefano, Bianchini; Gianluca, Crippa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/245399
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