Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
The following theorem is proven: suppose \(F:{\mathbb{R}}^ n\to {\mathbb{R}}\) be such that \(\nabla F\in L^{n,1}_{loc}\) in the distribution sense \((L^{n,1}\) being a Lorentz space). Then F is equivalent to a continuous function and differentiable a.e. The proof is based on a suitable new maximal inequality proven as a lemma.
scientific article; zbMATH DE number 3842495