Tightness of general \(C_{1,p}\) capacities on Banach space (Q1196571)

The authors consider a class of capacities on an infinite-dimensional Banach space with underlying measure \(\mu\) which generalize the \(C_{1,p}\)-capacities, \(p>1\), defined by Malliavin in the case of the Wiener space, but here the measure \(\mu\) need not be Gaussian in general. The capacities are defined in a purely analytic way in terms of the \(L^ p(\mu)\)-graph norm of an infinite-dimensional gradient operator. As the main result the authors prove the tightness of each of these capacities.