  We prove a frequency-independent bound on trigonometric functions of a class
of singular Gaussian random fields, which arise naturally from weak
universality problems for singular stochastic PDEs. This enables us to reduce
the regularity assumption on the nonlinearity of the microscopic models in KPZ
and dynamical $\Phi^4_3$ in [HX19] and [FG19] to that required by PDE
structures.
