The $\mathrm{\infty }$-Besov Capacity Problem

A theory of $\mathrm{\infty }$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\mathrm{\infty }$-Besov semi-norms, we obtain new restriction-extension inequalities and we characterize the point-wise multipliers acting on the $\mathrm{\infty }$-Besov spaces.