Functionals on Lipschitz spaces
We will study continuous linear functionals on Lipschitz spaces with a special focus on those belonging to canonical preduals, the Lipschitz-free spaces. First, we introduce a notion of support applicable to all continuous functionals. Then we will discuss their relation to measures. In particular, we will characterize the functionals represented by measures as those functionals that admit a Jordan-like decomposition into a positive and a negative part. We will see that such decomposition does not exist for all functionals in general, and we will identify the cases when it does.
The talk will be based on joint work with Ramón J. Aliaga.