On the Lp-differentiability of certain classes of functions

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