Accepted Paper

Inserted: 27 jan 2012
Last Updated: 14 jun 2012

Journal: Revista Matemática Iberoamericana
Year: 2012

Abstract:

We prove the $L^p$-differentiability at almost every point for convolution products on ${\bf R}^d$ 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 ${\bf R}^d$ whose curl and divergence are measures, and also for vector fields with bounded deformation.

Keywords: Approximate differentiability, Functions with bounded deformation, singular integrals, Sobolev functions, Lusin property, convolution products, Calderon-Zygmund decomposition, functions with bounded variation

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