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
ALBERTI, GIOVANNI;
2014-01-01
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.File in questo prodotto:
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