Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma

Daniel Spector, Jean Van Schaftingen

We prove a family of Sobolev inequalities of the form $$\Vert u{\Vert }_{L^{\frac{n}{n-1},1}({\mathbb{R}}^n,V)}\le \Vert A(D)u{\Vert }_{L^1({\mathbb{R}}^n,E)}$$ where $A (D) : C^\i…