On the Lᵖ-differentiability of certain classes of functions

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