Some natural subspaces and quotient spaces of $L^1$

Gilles Godefroy, Nicolas Lerner

We show that the space ${\text{Lip}}_0({\mathbb{R}}^n)$ is the dual space of $L^1({\mathbb{R}}^n;{\mathbb{R}}^n)/N$ where $N$ is the subspace of $L^{1}({\mathbb R}^{n}; {\mathbb R}…