On weak approximations of UU-statistics

This paper investigates weak convergence of UU-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying UU-statistic exists is relaxed to having 43 moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the classical two-moment condition).