The asymptotic distributions of $L_p$ functionals of weighted uniform quantile and empirical processes are studied. The asymptotic laws obtained are represented in terms of Gaussian and Poisson integrals.
"On the Distributions of $L_p$ Norms of Weighted Uniform Empirical and Quantile Processes." Ann. Probab. 16 (1) 142 - 161, January, 1988. https://doi.org/10.1214/aop/1176991890